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Concurrent lines when squares erected on sides of ABC

Source: Hungary-Israel, 1997

December 31, 2004
geometrycircumcircletrigonometry

Problem Statement

The three squares ACC1A′′ACC_{1}A'', ABB1′A′ABB_{1}'A', BCDEBCDE are constructed externally on the sides of a triangle ABCABC. Let PP be the center of the square BCDEBCDE. Prove that the lines A′CA'C, A′′BA''B, PAPA are concurrent.
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