







The center of a circle 
20191024 

From Patrick: I'm trying to find a quick calculation to find the center of the circle that will touch the 3 points of an isosceles triangle.
Known dimensions are length of the triangle base and the height from the top point to the middle of the base.
Thanks in advance,
Kind regards,
Patrick Answered by Penny Nom. 





The circumcentre of a triangle 
20160728 

From Raj: If the vertices of triangle ABC are A(4,1) B(1,2) C(4,3) then find coordinates of circumcentre of triangle Answered by Penny Nom. 





A cyclic quadrilateral 
20140328 

From Carly: Suppose ABCD is a cyclic quadrilateral, i.e A, B, C, and D are the points on a circle,
given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre
of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint.
Thank you. Answered by Chris Fisher. 





The circumcenter 
20121209 

From BandNerd: I need to find the circumcenter of the triangle with the coordinates A(0,0) B(12,6) and C(18,0). I do not understand how to solve it algebraically. Please help! Answered by Chris Fisher. 





Finding the circumcentre 
20120524 

From Glen: Hi,
I'm having trouble finding the circumcentre of these 3 coordinates A(1,1) B(10.5,1) and C(6,6).
I understand what circumcentre is but I cannot work out where it is.
Thanks very Much,
Glen Answered by Chris Fisher. 





The circumcentre and orthocentre of a triangle 
20120425 

From Nazrul: The circumcentre and orthocentre of a triangle is given. A point on a side of the triangle
given. A vertex of the triangle on the circumcircle is also given.
How can I draw the triangle?
Please Help me.
Thank you for answering my previous questions. Answered by Chris Fisher. 





The circumcentre, centroid and orthocentre of a triangle 
20120424 

From Nazrul: The circumcentre, centroid and orthocentre of a triangle is
given. The distance between circumcentre and orthocentre is also
given.
How can I draw the circle?
Please Help me. Answered by Chris Fisher. 





A circular cylinder circumscribed about a right prism 
20120125 

From Noriz: A cylinder is circumscribed about a right prism of altitude 12.6cm.
Find the volume of the cylinder if the base of the prism is an
isosceles triangle of sides 3cm by 3cm by 2cm.
Hope you can help me with this. Answered by Penny Nom. 





The center of an ellipse 
20090421 

From Nae: what is the ellipse center of 5x^2+3y^2=15 Answered by Stephen La Rocque. 





The centroid and circumcircle of a triangle 
20081209 

From prateet: in an equilateral triangle prove that the centroid and centre of the circumcircle coincide
here i am not clear about the concept of centroid and circumcircle
i cant understand how AGis 2/3 AD.
please help in details about the topic mentioned. Answered by Harley Weston. 





The centre and radius of a circle 
20080312 

From Ryan: hello and thank you for such a wonderful service.
This problem I think needs to be checked could you take a gander at it and tell me if i get it correct thanks
find the center and the radius of this circle x^2+y^2=8x2y+15=0
I cam up with center 2, 1/2 and a radius of 11 3/4 Answered by Harley Weston. 





Circumcentre of a triangle 
20071218 

From Kathryn: Find the coordinates of the circumcentre of the triangle whose vertices are:
(5, 3), (3, 1), (1, 5) Answered by Stephen La Rocque. 





Constructing the centre of a circle 
20071106 

From Carolyn: I have a line segment AB. I need to divide a segment into 3 parts that are congruent. Please help how to divide it. The answer that I was given previous was not the way the teacher wanted it.
I also need information on how to find the center of a circle given an arc. Answered by Penny Nom. 





Finding the center of an ellipse 
20070620 

From Sima: find the center of the ellipse with the equation 3x^2 +4y^2+18x32y5=0 Answered by Penny Nom. 





The orthcentre and the circumcentre 
20070405 

From Ruby: I have tried to do this question so many times, could you please, please,
please show me how to do it. I just can't get the answer:
What is the (i)Circumcentre and (ii)Orthocentre of the triangle with
vertices a(2,2) b(2,6) c(5,3)? It would be so great if you could show
me how to do this. Thanks in advance,
Ruby. Answered by Penny Nom. 





The centre and radius of a circle 
20070127 

From A student: x^2+y^2=121 is the equation of the Circle C
(1) Write down the center and the radius of C. Answered by Stephen La Rocque. 





The centre and radius of a circle 
20060402 

From Kaye: I need to calculate Dimension E and F. I am given A, B, C, (or over all A+B+C), D, G. The radius is one continuous unknown radius.
Example: A = 23.50
B = 35.50
C = 0.50
D = 11.50
G = 23.50
I have calculated this for angles but my mind is drawing a blank for the radius calculation. I can draw it but I need to put into Excel spreadsheet.
Answered by Harley Weston. 





A circle problem 
20060123 

From Matyan:
Find the standard equation of the circle that passes through the points (0,4) and (3,7) with center on the line
2xy+4=0.
I've tried substituting the two points to the general equation of a circle, but I can't solve it without a third equation. The problem here is I don't really know how to use the given line of 2xy+4=0. Please help. Thank you.
Answered by Penny Nom. 





The circle through three points 
20040706 

From Jim: I am a student trying to solve math problem. I'd like to calculate the radius of the circle that exactly fits any three points. If the points are (X1,Y1), (X2,Y2), and (X3,Y3), what is the radius of the circle that contains those three points? Answered by Penny Nom. 





The orthocentre 
20021017 

From Elsie:
 Find the orthocentre of the triangle with vertices at A(3,4), B(10, 3) and C(3,2).
 Find the distance of point X(3,8) from the line that passes through Y(2, 2) and Z (3, 2).
Answered by Chris Fisher. 

