MathDB
Point Inside Triangle

Source: Turkey EGMO TST 2015 P2

August 7, 2016
geometry

Problem Statement

Let DD be the midpoint of the side BCBC of a triangle ABCABC and PP be a point inside the ABDABD satisfying ∠PAD=90∘−∠PBD=∠CAD\angle PAD=90^\circ - \angle PBD=\angle CAD. Prove that ∠PQB=∠BAC\angle PQB=\angle BAC, where QQ is the intersection point of the lines PCPC and ADAD.
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