MathDB
Triangle

Source: Turkey National Mathematical Olympiad 2018

December 2, 2018
geometry

Problem Statement

Let PP be a point in the interior of the triangle ABCABC. The lines APAP, BPBP, and CPCP intersect the sides BCBC, CACA, and ABAB at D,ED,E, and FF, respectively. A point QQ is taken on the ray [BE[BE such that E∈[BQ]E\in [BQ] and m(EDQ^)=m(BDF^)m(\widehat{EDQ})=m(\widehat{BDF}). If BEBE and ADAD are perpendicular, and ∣DQ∣=2∣BD∣|DQ|=2|BD|, prove that m(FDE^)=60∘m(\widehat{FDE})=60^\circ.
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