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Source: 2021 Korea Winter Program Test2 Day2 #6

February 17, 2021
geometry

Problem Statement

The acute triangle ABCABC satisfies AB‾<BC‾<CA‾\overline {AB}<\overline {BC}<\overline {CA}. Denote the foot of perpendicular from A,B,CA,B,C to opposing sides as D,E,FD,E,F. Let PP a foot of perpendicular from FF to DEDE, and Q(≠F)Q(\neq F) a intersection point of line FPFP and circumcircle of BDFBDF. Prove that ∠PBQ=∠PAD\angle PBQ=\angle PAD.
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