MathDB
Convex quadrilateral

Source: Iran TST 2004

January 9, 2009
geometrycircumcircleratioprojective geometrygeometry proposed

Problem Statement

Suppose that ABCD ABCD is a convex quadrilateral. Let F \equal{} AB\cap CD, E \equal{} AD\cap BC and T \equal{} AC\cap BD. Suppose that A,B,T,E A,B,T,E lie on a circle which intersects with EF EF at P P. Prove that if M M is midpoint of AB AB, then \angle APM \equal{} \angle BPT.
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