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PAMO Problem 4: Easy geometry

Source: 2018 Pan-African Mathematics Olympiad

July 3, 2018
geometrycyclic quadrilateralAngle Chasing

Problem Statement

Given a triangle ABCABC, let DD be the intersection of the line through AA perpendicular to ABAB, and the line through BB perpendicular to BCBC. Let PP be a point inside the triangle. Show that DAPBDAPB is cyclic if and only if ∠BAP=∠CBP\angle BAP = \angle CBP.
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