MathDB
Tricky triangle problem

Source: Iran 2002

August 20, 2005
trigonometrygeometryratiogeometric transformationreflectioninvarianttrapezoid

Problem Statement

Let M M and N N be points on the side BC BC of triangle ABC ABC, with the point M M lying on the segment BN BN, such that BM \equal{} CN. Let P P and Q Q be points on the segments AN AN and AM AM, respectively, such that \measuredangle PMC \equal{}\measuredangle MAB and \measuredangle QNB \equal{}\measuredangle NAC. Prove that \measuredangle QBC \equal{}\measuredangle PCB.
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