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Rectangles erected on sides of a triangle; a concurrence

Source: Bundeswettbewerb Mathematik (Germany) 1996, round 2, problem 3

December 31, 2004
geometryrectanglecircumcirclegeometric transformationreflectionhomothetyvector

Problem Statement

Let ABCABC be a triangle, and erect three rectangles ABB1A2ABB_1A_2, BCC1B2BCC_1B_2, CAA1C2CAA_1C_2 externally on its sides ABAB, BCBC, CACA, respectively. Prove that the perpendicular bisectors of the segments A1A2A_1A_2, B1B2B_1B_2, C1C2C_1C_2 are concurrent.
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