







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. 





If a parallelogram is a cyclic quadrilateral then it is a rectangle 
20120201 

From Kim: Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle.
Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20110815 

From Tim: Hi! I've been working on this for a while and I'm quite stuck. If anyone can help that would be great.
The sides BC and AD of a quadrilateral ABCD are parallel. A circle meets the side AB at B and E and the side CD at C and F. Prove that the quadrilateral AEFD is cyclic. Answered by Chris Fisher. 





A cyclic quadrilateral 
20090123 

From Murtaza: Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20061120 

From Namrata: If two sides of a cyclic quadrilateral are parallel, prove that (1) remaining two sides are equal, (2) both diagonals are equal. Answered by Penny Nom. 

