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CMO 2017 P4

Source: Canadian Mathematical Olympiad 2017

March 31, 2017
geometryparallelogram

Problem Statement

Let ABCDABCD be a parallelogram. Points PP and QQ lie inside ABCDABCD such that △ABP\bigtriangleup ABP and △BCQ\bigtriangleup{BCQ} are equilateral. Prove that the intersection of the line through PP perpendicular to PDPD and the line through QQ perpendicular to DQDQ lies on the altitude from BB in △ABC\bigtriangleup{ABC}.
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