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Orthogonal projections and areas

Source: Polish MO

February 25, 2017
geometry

Problem Statement

In an acute triangle ABCABC the bisector of ∠BAC\angle BAC crosses BCBC at DD. Points PP and QQ are orthogonal projections of DD on lines ABAB and ACAC. Prove that [APQ]=[BCQP][APQ]=[BCQP] if and only if the circumcenter of ABCABC lies on PQPQ.
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