MathDB
cyclic quadrilateral (maybe posted before)

Source: Austria 1997

July 11, 2009
geometryparallelogramgeometry unsolved

Problem Statement

Let be given a triangle ABC ABC. Points P P on side AC AC and Y Y on the production of CB CB beyond B B are chosen so that Y Y subtends equal angles with AP AP and PC PC. Similarly, Q Q on side BC BC and X X on the production of AC AC beyond C C are such that X X subtends equal angles with BQ BQ and QC QC. Lines YP YP and XB XB meet at R R, XQ XQ and YA YA meet at S S, and XB XB and YA YA meet at D D. Prove that PQRS PQRS is a parallelogram if and only if ACBD ACBD is a cyclic quadrilateral.
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