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4 Right Angles

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 9.3

April 5, 2023
geometryaltitudes

Problem Statement

You are given an acute triangle ABCABC with circumcircle ω\omega. Points FF on ACAC, EE on ABAB and P,QP, Q on ω\omega are chosen so that ∠AFB=∠AEC=∠APE=∠AQF=90∘\angle AFB = \angle AEC = \angle APE = \angle AQF = 90^\circ. Show that lines BC,EF,PQBC, EF, PQ are concurrent or parallel.
Proposed by Fedir Yudin
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