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Source: Chinese TST 2009 5th P2

April 4, 2009
geometrycircumcirclegeometric transformationreflectionratiotrigonometrygeometry proposed

Problem Statement

In acute triangle ABC, ABC, points P,Q P,Q lie on its sidelines AB,AC, AB,AC, respectively. The circumcircle of triangle ABC ABC intersects of triangle APQ APQ at X X (different from A A). Let Y Y be the reflection of X X in line PQ. PQ. Given PX>PB. PX>PB. Prove that S△XPQ>S△YBC. S_{\bigtriangleup XPQ}>S_{\bigtriangleup YBC}. Where S△XYZ S_{\bigtriangleup XYZ} denotes the area of triangle XYZ. XYZ.
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