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cyclic quadrilateral

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A cyclic quadrilateral 2014-03-28
Carly pose la question :
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.

Chris Fisher lui répond.
If a parallelogram is a cyclic quadrilateral then it is a rectangle 2012-02-01
Kim pose la question :
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.
Robert Dawson and Chris Fisher lui répond.
A cyclic quadrilateral 2011-08-15
Tim pose la question :
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.
Chris Fisher lui répond.
A cyclic quadrilateral 2009-01-23
Murtaza pose la question :
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.
Robert Dawson and Chris Fisher lui répond.
A cyclic quadrilateral 2006-11-20
Namrata pose la question :
If two sides of a cyclic quadrilateral are parallel, prove that
(1) remaining two sides are equal,
(2) both diagonals are equal.

Penny Nom lui répond.
 
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