







Heights at various points along an arc 
20160415 

From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature.
How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6 Answered by Penny Nom. 





A circle and a chord 
20160310 

From Mujtaba: The distance of a chord of length 16 cm, from the centre of the circle of diameter 20 cm Answered by Penny Nom. 





A chord of a circle, the central angle and the radius 
20160126 

From Nishan: If chord length is given along with angle then how to calculate the radius. Answered by Penny Nom. 





Reinforced steel mesh in a circular foundation 
20150822 

From Padmesh: in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference Answered by Penny Nom. 





The number of possible musical notes using an nkey instrument 
20150504 

From Farihin: Lets say that i have keys, and each key is for notes of a musical instrument,
So i wanted to find out the number of notes i can get for a certain number keys,
of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100.
Notes in real life is not as such, but ignore reality.
I tried doing this but i can't seem to find a formula for it.
For example, i have 4 keys, say A, B, C, and D.
so, for notes that uses one key are 4, which is A, B, C, and D themselves.
for notes that uses two keys are 6,
AB, AC, AD, BC, BD and CD.
for notes that uses three keys are 4,
ABC, ABD, ACD and BCD.
lastly for notes that uses all four keys is 1, ABCD.
So, the total will be 4+6+4+1=15#
The nth term for the first equation is n, the second is [(n^2)n]/2
the third and the fourth, i don't know but the final answer should be like,
n + [(n^2)n]/2 + [3rd] + [4th]
Sorry for the long question though... Answered by Penny Nom. 





Two concentric circles 
20150421 

From Juniper: Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment? Answered by Penny Nom. 





A circle and a chord 
20150207 

From Dakota: If the diameter of a circle is 48 cm, find the shortest distance from a chord of length 34 cm to the center of the circle Answered by Penny Nom. 





Two chords in a circle 
20140913 

From Carlos: Find the length of the radius of a circle in which a
chord of length 6 units is twice as far from the
center as a chord of length 12 units Answered by Penny Nom. 





A chord and an arc of a circle 
20140806 

From Luis: Hello I am trying to figure out how to get chord lengths of quarter points for a circle. I work with large diameter circles and I need to be able to find chord length from 0 degrees to 90 degrees, 0 degrees to 270 degrees, 270 degrees to 180 degrees and 90 degrees to 180 degrees. Can you please use 100ft. diameter as example and work out the problem. I'm sorry if I use wrong terminology, I'm really bad at math . Thank you in advance for your time and help I really appreciate it. Answered by Harley Weston. 





A chord length of 2 cm 
20140313 

From prema: I am having only chord length as 2cm. how to find arc length and degree Answered by Penny Nom. 





Parallel chords 
20140306 

From Raj: AB andCD are two chords which are in the same side of the circle.The length of AB=12 and CD= 24.if the distance between them is 4 then find their radius. Pls help me I just believe on you guys I am having my exam after 3 days Answered by p. 





Two parallel chords of a circle 
20130730 

From Don: two parallel chords of a circle AB and CD on the same side from the center measure 6cm and 11 cm respectively. The distance between the 2 chords is 3 cm. Find the radius Answered by Penny Nom. 





A circle and a chord 
20130514 

From yashvardhan: A circle which radius 13cm. Find the length of the chord which is 5 cm away from center Answered by Penny Nom. 





A circle, a chord and an arc 
20130416 

From Tim: Morning,
I was told the chord is 3000mm and the depth of chord is 300mm, I can
find the radius,(1500 squared + 300 Squared) Divided by (300 + 300)
but don't know how to calculate the length of the circle defined by the chord.
Regards
Tim
Answered by Penny Nom. 





The length and depth of a chord 
20120816 

From Tim: Can I find the radius of a circle, if I have a chord of 2400mm, and a depth
between the center of the chord and the perimeter of the circle of 150mm ?
Thanks
Tim Answered by Penny Nom. 





The shortest chord 
20120726 

From ANJANA: AB is a diameter of a circle.
C is a point in AB such that CA = 9 cm and CB = 25 cm.
Find the length of the shortest chord through C. Answered by Chris Fisher. 





The depth of a chord 
20120516 

From Tim: For a circle of Diameter 12 Mtrs, I have a chord length of 2 Mtrs,
How can i calculate the distance from the middle of the chord to the
perimeter of the circle Answered by Penny Nom. 





A common chord to two circles 
20120422 

From Nicole: What is a common chord between two circles and how is it found in the problem: Two circles intersect and have a common chord, the radii of the circles are 13 and 15, the distance between the circle's centers is 14, find the common chord. Answered by Penny Nom. 





A circle and a chord 
20120211 

From Sophia: The diagram shows a circle with a chord that is 10cm long. The middle of the chord is 12cm from the centre of the circle. Calculate the radius.
Chord length is 10cm.
The distance from the centre to chord is 12 cm. Answered by Penny Nom. 





Two circles 
20120208 

From crisfe: find the point where the common cord of the circles x2+y2=25, x2+y212x6y+35=0 process there line centers. what point they intercepts? Answered by Penny Nom. 





Two parallel chords 
20111204 

From violet: Two parallel chords of a circle AB and CD on the same side of the centre measure 6 cm and 11 cm respectively. Find the radius. Answered by Chris Fisher and Walter Whiteley. 





The length of an arc 
20110824 

From nuel: Is there any formula to calculate the arc length from only the chord length and angle between the chord and tangent of the arc at its endpoint ? Answered by Penny Nom. 





The length of a chord 
20110425 

From G: A 120 degree central angle intercepts a circle at the points A and B. The radius of the circle is 10 cm. Find the length of chord AB. Answered by Penny Nom. 





A region bounded by a chord and an arc 
20110228 

From Gene: find the area of a segment bounded by a chord and a 45 degree arc of a 36" circle Answered by Robert Dawson. 





Two chords in a circle 
20101202 

From girma: one chord of a circle is 8cm long and it's distance from the center is 4cm long.what will be the length of another chord, of the same circle ,which is 2cm from the center Answered by Penny Nom. 





Two perpendicular chords 
20100911 

From edwin: two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. I do not a have clue on how to do it so can you please help me with it Answered by Robert Dawson. 





Arc length and Chord length 
20100313 

From Darryl: Is there a formula to determine the chord length of an arc knowing only the arc length and the arc depth (sagitta)? I know you can't find the radius with only these two inputs, but can you find the chord length? Answered by Harley Weston. 





The distance from a chord to an arc 
20100211 

From matt: hello, I have to layout a radius without being able to pull from the center my radius is 3819.53 feet and i have a chord length of 275.59 feet if i broke that up into 25.05 feet sections how would i calculate the lengths from my chord to that radius? Answered by Robert Dawson. 





A tunnel from Toronto to Montreal 
20100125 

From Dave: I want to make a tunnel from Toronto to Montreal (for example)
Something like this
http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/grant1.html

My coordinates are 45.442455,73.861340 (Montreal) and 43.442455, 79.861340 (Toronto)
I need to know how to find arc distance, chord distance and radius
What websites can i find for this subject
Google has many but they are useless (blah blah) websites
LOL
Thanks Answered by Chris Fisher and Robert Dawson. 





The height of an arch 
20100102 

From kamer: given the radius 1.696 also the cord length 1.958 find the height between the cord and the arch. Answered by Penny Nom. 





A question from a boat builder 
20100101 

From Grant: I am a boat builder, trying to lay out shape of side's elevation.
My question is, how do I define the length of a circle's radius, if I know the chord length
(20 ft) and the segment of the radius between the chord and the circle is known (7 inches)? Answered by Penny Nom. 





Chord length given the length & radius of an arc 
20091231 

From Wayne: Given the length & radius of an arc, is there a formula that will accurately calculate the chord length?
I'm an architectural designer, and would need it explained in layman's terms. Thank you.
Wayne Answered by Penny Nom. 





Sagitta 
20090910 

From Robert: Can you please tell me if there is a formula to figure out the Sagitta of an
arc when you know the radius, chord length, and arc length? Answered by Chris Fisher and Harley Weston. 





Find the central angle 
20090818 

From Larissa: In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem. Answered by Harley Weston. 





Two chords 
20090711 

From Sarah: Two parallel chords in the same circle have lengths of 30 cm and 48 cm. The circle has a radius of 25 cm. How far apart are the chords? Answered by Penny Nom. 





Arc length 
20090710 

From farhad: hi
i need to measure length of arc by having only two measurements, first the length of the chord and
the height of the curve.
if i have a simple calculator that haven't sin cos tang (i want to calculate it in my mind) Answered by Stephen La Rocque. 





A circle and a chord 
20090710 

From Paul: I have three known points. X1,Y1 = 0,0 X2,Y2 = 3,1 and X3,Y3 = 10,0. Given these three points, how do I find the height from the center of the 10' chord to the circle's circumference above? Answered by Stephen La Rocque and Harley Weston. 





The central angle of a chord 
20090406 

From Dale: How do I find the central angle if I only have the cord length and radius. Answered by Harley Weston. 





The length of an arc 
20090404 

From Dale: If I have the length of the chord and the height of the arc can I find the arc length with these dimensions? Answered by Harley Weston. 





The length of a chord 
20090320 

From shirley: show that the chord is equal to two times the radius time the sin of theta/2.
The chord is connected to the two radii and theta is a central angle between the two radii Answered by Penny Nom. 





Two chords in a circle 
20090119 

From azlaan: prove that line joining the midpoint of 2 equal chords substain equal angle with the chord? Answered by Robert Dawson. 





Parallel distances from arc of circle to its chord 
20090116 

From Roger: Give the length of a chord of a circle and the height of the arc, how do I
find the lengths of equally spaced parallel lines drawn from the chord to
the arc. (Think of the lengths of vertical slats in an archtopped bed head
board.) Answered by Chris Fisher and Stephen La Rocque. 





A chord 
20090101 

From Deepa: Why in a circle,a chord is called as the longest diameter?
(A chord does not passes through the centre of the circle but a diameter passes through the centre) Answered by Penny Nom. 





A circle and a chord 
20081117 

From Lydz: The circle has a radius of 8cm
The chord is 13cm long.
Find the distance from the centre of the circle, to the chord. Answered by Penny Nom. 





A circle and a chord 
20081113 

From jane: the center of a circle is at (3,2) and its radius is 7. find the length of the chord, which is bisected at (3,1). Answered by Penny Nom. 





An arc and an angle 
20081005 

From Cory: I have a chord length of 150'. From the left starting point, I know that
30' right of starting point is 9' in height. This would be the top of the arc.
What is the arc in degrees and can anyone display an image to help me
understand? Answered by Penny Nom. 





The area of an arched transom 
20080928 

From Ivan: What is the formula for figuring out the square footage of arched transom windows & doors? Answered by Harley Weston. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Irregular polygon and Circle that Intersects All Sides 
20080820 

From Xetro: Hi,
Suppose you have an irregular polygon(convex or concave) with n > 3 sides.
The question is  Find some circle that will cut(in limiting case  touch) all the sides of that polygon.
It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it.
How to find such a circle? or how to decide if such circle even exists?
What if those segments do not form a polygon but are some arbitrary segments ?
Really want to know how to do it................
Thanks a lot..
Regards,
Xetro Answered by Janice Cotcher. 





Subdividing a chord 
20080818 

From austin: Here is my question. Imagine I have a circle of known radius 25 feet, and a
chord with a mid point height of 6 inches from a central point on the chord
to the circumference of the circle. I wish to divide this chord into a
number of equal divisions. How can I calculate the measurement of the
perpendicular line at each division of the chord to the circumference and at
a 90 degrees at each division Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





The length of an arc 
20080714 

From Chris: trying to find the length of an arc or segment of a circle when
the radius or circumference is unknown
take a circle, put a line across the circle label it A /B /C
A and C are the end points, B is the middle
line length is 86. From B to the side of circle is 16. Label that point D
need to find the length of A D C Answered by Penny Nom. 





Chords and arcs 
20080711 

From Ronnie: We are trying to build a semi life size ark decoration , and we are trying to cut the sides out . The curved sides and we can't figure our radius , all we know is that our chord length is 24ft. any suggestions on how to find the radius or maybe even the arc length or circumference or diameter? Answered by Harley Weston. 





One chord is twice as long as another 
20080530 

From Stacey: In a circle, If one chord is twice as long as another, is the longer chord's arc also twice the size of the smaller chord? True or False Answered by Chris Fisher. 





The distance from the chord to the centre 
20080504 

From sle: What is the method for figuring this type of question out?
in a circle whose radius is 25, a chord has a length of 40. find the distance of this chord from the center of the circle Answered by Penny Nom. 





Two overlapping circles 
20080426 

From Michelle: Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Answered by Penny Nom and Walter Whiteley. 





Chord, radius, arc length and central angle 
20080415 

From Cindy: There is a railroad curve with a chord length of 2000 ft. and a central angle of 35 degrees. What is the radius and arc length of the circular arc? Answered by Stephen La Rocque. 





Finding the radius when only given chord length 
20080403 

From Lorraine: There are two chords in a circle, an 8 inch chord and a 10 inch chord. The 8 inch chord
is twice the distance from the center as the 10 inch chord. What is the radius? Answered by Stephen La Rocque. 





A common chord to two circles 
20080309 

From shubha: please help me out with this problem.
find the length of the common chord of the intersecting circles x2+y24x5=0
and x2+y22x+8y+9=0 Answered by Stephen La Rocque. 





A chord of a circle 
20080207 

From Mahesh: find the length of the cord intercepted by a circle with equation X2 +Y2 6X+4Y12=0 with a line of equation 4X3Y+2=0
Pl help me solve this problem
thanks
MNK Answered by Stephen La Rocque. 





How would one find the radius? 
20071229 

From Ned: Given an arc with length of 192 inches (don't know chord length),
and arc height of 6 inches, how would one find the radius? Answered by Stephen La Rocque and Harley Weston. 





The radius of an arch 
20071110 

From Mark: How do you determine the raduis or diameter of a circle based on the folowing information:
1. The distance along the circle between two points is 35'2". This creates an arch.
2. The (chord) distance between the two points is 30'8".
3. The distance from the center of the chord (on a 90 degree) to the arch is 6'10 3/4". Answered by Harley Weston. 





Given the arc length and chord length, what is the radius? 
20071010 

From Wayne: I have the actual length of an arc plus the length of the cord. How do I determine the radius of the arc. Answered by Harley Weston. 





Finding radius given chord length and distance to center 
20071004 

From Venus: a chord of 48mm long is 7mm from the center of the circle. What is the radius of the circle? Answered by Stephen La Rocque. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





The area of a circle knowing only the length of a chord 
20070905 

From James: I need some help in the right directions with a problem. I was presented with a problem where I need to find the area of a circle knowing only the length of a chord.
the is a circle in the center of a larger circle (which the size of either could change) the only thing that matter is that the chord is 100 ft long and rests on top of the smaller circle. Answered by Stephen la Rocque and Brennan Yaremko. 





A chord of a parabola 
20070817 

From Robin: I am going to show that the chord PtPt' of the parabola has the equation 2xy(t+t')+2att'
A point on the parabola can be represented as Pt= (at2, 2at). Answered by Penny Nom. 





Chords 
20070808 

From HIMANSHU: we know that every straight line is the chord of a big circle. i have a circle
with radius 3.5feet. I want to know what is the length of the chord,
which would be a straight line. Answered by Stephen La Rocque. 





Two chords in a circle 
20070729 

From Jerry: Points A and C lie on the circumference of a circle. B is a point inside the circle. When produced, AB and CB meet the circumference at points E and D respectively. Prove that AB = CB, then EB = BD. Answered by Stephen La Rocque. 





Circles and chords 
20070315 

From Henry: Where do you place a chord in a circle such that it divides the area
of the circle 1/3 and 2/3? Also, what is the length of the chord? Answered by Stephen La Rocque. 





Chords and arc lengths 
20070308 

From Angela: my dad, who is a welder, asked me a question pertaining to chords and points on an arc to which I cannot for the life of me find an answer or an equation. if you could help, it would be much appreciated. I am sending an attachment of the problem. Answered by Stephen La Rocque. 





Chord length 
20061101 

From Tony: how do i find a chord length when all i have is arc length (13.633m) and the radius (89.500m) Answered by Stephen La Rocque. 





Find the radius knowing the chord length and... 
20060728 

From Jim: If I know the length of a chord and its distance from the diameter, how do I calculate the radius of the circle?
Answered by Stephen La Rocque. 





The chord length of a polygon 
20060614 

From Krishna: I have to find out the chord length of a polygon  Tetradecagon ! The Radius of the Circle is 11.5 Cms. The Circle is intersepted by 14 arcs. Then how to find out the chord length? Answered by Stephen La Rocque. 





The length of a chord 
20051103 

From Sue: How do you determine the length of a chord when given the diameter of the circle (1.6m) and that the angle = 7π/8 Answered by Penny Nom. 





A line that intersects a circle 
20051018 

From Bruce: I would like to solve the following problem illustrated below. How do you calculate the length of a line that intersects a circle. Answered by Penny Nom. 





How would I find the length of the radius? 
20051015 

From Stace: If given the length of a chord (121") and the distance from the midpoint of the arc to the midpoint of a chord (12"), how would I find the length of the radius?
Answered by Penny Nom. 





The length of a circle's chord 
20050928 

From A homebuilder: find the length of a circle's chord with a known arc length and radius/diameter lengths. Answered by Penny Nom. 





The length of a chord 
20050908 

From A student: how do you find the length of a chord given the angle and radius of the circle Answered by Penny Nom. 





Given only the length of an arc & the length of its chord find the radius? 
20050907 

From Robert: Given only the length of an arc (72) & the length of its cord (71), how to find the radius? Answered by Penny Nom. 





The radius of an arc 
20050819 

From Jared: I need to be able to calculate the radius of an arc on an existing structure (Supports for Fifth Ave Dimensional Text). I have the overall length of this structure, but, the complication I believe lies in the fact that it is a curve mounted onto a flat section of wall on either side of a very mild curve, therefore, measuring the middle of the wall to the top of the arc does me little good...The reason I need this is to be able to replicate the above curve on a similar structure to be mounted below it...Also, because the client wants the structure mounted on the inside of the opening below the existing, the beginning and end point of the new structure would be lower than the existing, so, I do not believe that it is possible to exactly replicate the radius of the above curve? Answered by Penny. 





The length of a chord 
20050113 

From A parent: Does anyone have a formula for calculating the chord length for a segment of a circle when you know the radius and the enclosed angle or radian ? Answered by Penny Nom. 





Arcs and chords 
20050109 

From Aniesha: A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





The length of a chord 
20031103 

From David: When Radius=400.00' and Arc=130.58' what is the Cord distance in feet? Answered by Penny Nom. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





The length of an arc 
20030224 

From Gavin: does anyone have a formula for calculating the length of an arc if I have the circle radius and the cord length of the arc?? Answered by Penny Nom. 





The length of an arc 
20021127 

From Nancy: If all I have is the length between 2 ends of an arc (72"), how do I find the length of the arc at its apex and the radius? Answered by Penny Nom. 





Subdividing a circle 
20021111 

From David: Say you have a cirlcle. Then you draw 2 dots on the circle. Then you connect the dots with lines. The circle is divided into 2 parts. If you do the same with 3 dots and connect each dot to each dot with a line then you get a circle with 4 parts. 4 dots with lines connecting all (6 lines) = 8 parts.... Answered by Claude Tardif. 





How would you find the length of the chord? 
20021031 

From A draftsperson: If given the length of an arc and the distance from the midpoint of the arc to the midpoint of a chord, how would you find the length of the chord and the radius of the arc. The chords endpoints are the same as the the arcs endpoints. Answered by Penny Nom. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Answered by Penny Nom. 





Three chords 
20010628 

From Paul: AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. Answered by Harley Weston. 





A chord length 
20001017 

From Al Paas: How to determine the length of a chord given the diameter of the circle and the maximum distance from the chord to The circle? Answered by Chris Fisher. 





A parabola problem 
20000323 

From Morin: I need to prove that if parabola x^{2}=4py has a chord (not necessarily a focal chord) intersecting it at points A and B, with tangents to the parabola at points A and B that intersect at C, then a line drawn through C and the midpoint of the chord M is parallel to the yaxis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM. Answered by Penny Nom. 





Two Chords 
19980929 

From Jennifer Cane: Question: two parallel chords of a circle, AB and CD, have lengths of 10 cm and 17 cm respectively. The diameter of the circle is 21 cm. Find the shortest distance between the chords. Answered by Harley Weston. 





The Length of a Chord. 
19970726 

From Nathan Arthur: Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Answered by Chris Fisher. 





Some Circle Questions. 
19970225 

From Staci Vawser: A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Answered by Harley Weston. 





Common Area of two sectors. 
19961106 

From Lynda Mow: How do I find the area common to two intersecting circles of radii 8 ft and 10 ft if their common chord is 10 ft long? Answered by Penny Nom. 





La longueur d'une corde 
20030122 

From Un eleve: Existetil une formule permettant de calculer la longueur d'une corde quelquonque d'un cercle connaissant uniquement le rayon de celuici? Si oui quelle estelle? Answered by Claude Tardif. 

