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Equal angles (a very old problem)

Source: ISL 2007, G3, VAIMO 2008, P5

July 13, 2008
geometrytrapezoidhomothetyIMO ShortlistDDIT

Problem Statement

The diagonals of a trapezoid ABCD ABCD intersect at point P P. Point Q Q lies between the parallel lines BC BC and AD AD such that \angle AQD \equal{} \angle CQB, and line CD CD separates points P P and Q Q. Prove that \angle BQP \equal{} \angle DAQ.
Author: Vyacheslav Yasinskiy, Ukraine
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