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Only squares staisfy these conditions

Source: Russian TST 2015, Day 10 P1 (Group NG), P2 (Groups A & B)

April 21, 2023
geometrysquare

Problem Statement

The points A′,B′,C′,D′A', B', C', D' are selected respectively on the sides AB,BC,CD,DAAB, BC, CD, DA of the cyclic quadrilateral ABCDABCD. It is known that AA′=BB′=CC′=DD′AA' = BB' = CC' = DD' and ∠AA′D′=∠BB′A′=∠CC′B′=∠DD′C′.\angle AA'D' =\angle BB'A' =\angle CC'B' =\angle DD'C'.Prove that ABCDABCD is a square.
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