







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. 





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 centroid of a polygon 
20071229 

From David: I am playing around with an idea. I've read previous answers to questions
(using surveyor calculation methods) related to finding the area of an irregular
shape parcel of land (or irregular polygon). Is there a formula or method for
calculating the centroid (midpoint) for this type of polygon. I've seen plenty
of methods for calculating the midpoint for a triangle or regular shape poloygon
but few for an irregular shape polygon such as a parcel of land. Thanks... Answered by Harley Weston. 





Find the centroid 
20071126 

From josh: vertices X(2,6) Y(4,10) Z(14,6) find the coordinates of the centroid Answered by Stephen La Rocque. 





Return on investment 
20071102 

From Julie: Hi  I'm trying to figure out what my ROI ( Return on my investment) is for a particular product I purchased. My investment cost was $4100 and my savings as a result of this investment was $34,170. How can I figure out what my ROI was on this product. Thanks much for your help! Answered by Penny Nom. 





A perpendicular intersection of two barrel vaults 
20060721 

From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings.
A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults).
A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semicircular arch.
The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault.
Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle. 





The centroid of a triangle 
20060118 

From Andrea: I am trying to find the centriod of a triangle. I have been given the three vertices of the triangle: A (25, 20), B (5, 40), and C (15, 30). I believe I calculated the correct midpoints: AB(E) (5, 5), BC(D) (5, 5), and AC(F) (15, 30). When I graphed these points I came up with the solution (5, 10), but I can't seem to write the answer out (equations of the lines, etc) correctly. Any help would be greatly appreciated! Answered by Penny Nom. 





The centroid of a triangle 
20050407 

From Maria: Q3)find the coordinates of the centroid of triangle ABC
i want your help here to solve the 3rd question i got stuck. Answered by Penny Nom. 





Vectors in three space 
20041030 

From Jo: I have two questions that I just cannot visulise and dont know how to get started on them..!
1. Ship X is sailing North at 4m/s and Ship Y is sailing due East at 3m/s. A sailor on Ship X climbs a vertical pole at 1/2 m/s. What is the velocity of the sailor on Ship X relative to an observer on Ship Y? State it's magnitude and direction.
Not sure where to start with this one...
2. Show, using vectors, that for any tetrahedron, the segments joining the midpoints of the opposite edges are concurrent.
i know what a tetradedron is, and what I am proving but do I solve simultaneously for a specific case?? Answered by Walter Whiteley. 





The point where all the medians meet 
20040225 

From A student: What's the name of the point where all the medians meet? Answered by Penny Nom. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. Answered by Harley Weston. 





Two sides and a bisectrix. 
19981111 

From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher. 





Volumes 
19980829 

From Lorraine Wall: Consider the region in the first quadrant bounded by the x and y axes, the vertical line x=3 and the curve y = 1 / (x squared + 3). Determine the volume of the solid by rotating this region about the xaxis. Now that is the first part. I then have to find the coordinates of the centroid of the solid by rotating this region about the xaxis. Thanks. Lorraine Answered by Harley Weston. 





Un système de plusieurs équations et plusieurs inconnues 
20090122 

From Cédrick: J'ai un problème écrit à résoudre estce que vous pouvez m'aider ?
Le premier est le tiers de la somme des deux autres.
La somme du premier et du deuxième est 13.
Le produit du deuxième et du troisième est 56.
Réponse: Le premier nombre est___________________
Le deuxième nombre est _________________
Le troisième nombre est _________________
Answered by PierreLouis Gagnon, Antoine Letarte at Claude Tardif. 





Marie achète un croissant et une tartelette 
20040201 

From M. et Mme Simoneton: Marie achète un croissant et une tartelette. Elle paie 1,64 €
Isabelle achète un croissant et un pain au chocolat. Elle paie 1,51 €
Marc achète un poain au chocolat et une tartelette. Elle paie 1,77 €
Trouver le prix d'un croissant, d'une tartelette et d'un pain au chocolat.
Answered by Claude Tardif. 





Les 3 maisons 
20031116 

From Amandine: Sur la figure cicontre on peut voir 3 maisons A, B et C nouvellement construites. Toutes les 3 doivent être reliées au gaz, à l'eau et à l'électricité. Cependant, tous ces raccordements doivent impérativement avoir lieu dans un même plan et les câbles et autres canalisations ne peuvent pas se croiser. Comment doiton s'y prendre pour relier les 3 maisons à l'eau, au gaz et à l'électricité? Answered by Claude Tardif. 

