5 items are filed under this topic.








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 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 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 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. 





A geometry proof 
20010418 

From Melissa: Extend the bisectors of angle A, angle B, and angle C of triangle ABC to meet the circumcircle at points X, Y, and Z respectively. Show that I is the orthocenter of triangle XYZ. Answered by Chris Fisher. 


