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The best length condition you'll ever see

Source: USAMO 2019 Problem 2 and JMO 2019 Problem 3, by Ankan Bhattacharya

April 17, 2019
USA(J)MOUSAMOHi

Problem Statement

Let ABCDABCD be a cyclic quadrilateral satisfying AD2+BC2=AB2AD^2 + BC^2 = AB^2. The diagonals of ABCDABCD intersect at EE. Let PP be a point on side AB‾\overline{AB} satisfying ∠APD=∠BPC\angle APD = \angle BPC. Show that line PEPE bisects CD‾\overline{CD}.
Proposed by Ankan Bhattacharya
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