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AF is perpendicular to DE wanted

Source: 2021 Turkey JBMO TST P1

May 23, 2021
geometrycirclesperpendicular linesTurkeyJunior

Problem Statement

In an acute-angled triangle ABCABC, the circle with diameter [AB][AB] intersects the altitude drawn from vertex CC at a point DD and the circle with diameter [AC][AC] intersects the altitude drawn from vertex BB at a point EE. Let the lines BDBD and CECE intersect at FF. Prove that AF⊥DEAF\perp DE
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