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Prove the perpendicularity

Source: Turkey JBMO TST 2024 P1

May 13, 2024
geometry

Problem Statement

In the acute-angled triangle ABCABC, PP is the midpoint of segment BCBC and the point KK is the foot of the altitude from AA. DD is a point on segment APAP such that ∠BDC=90\angle BDC=90. Let (ADK)∩BC=E(ADK) \cap BC=E and (ABC)∩AE=F(ABC) \cap AE=F. Prove that ∠AFD=90\angle AFD=90.
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