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| Math Central | Quandaries & Queries |
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Question from Tim, a student: 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. |
Tim,
You should know the theorem:
If the points PQRS lie in that order on a circle then each pair of opposite angles add up to 180 degrees, and conversely, if in a quadrilateral PQRS the angles at P and at R sum to 180 then the four points lie in the order P,Q,R,S around a circle.
The statement of your problem says that BCFE lie on a circle in that order, so the angles at B and F sum to 180; it is your job to prove that in quadrilateral AEFD the angles at F and at A sum to 180.
Chris
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