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3 perpendiculars are concurrent. defined by intersection of // and circumcircle

Source: Sharygin 2011 Final 8.3

December 13, 2018
geometryperpendicularconcurrencyconcurrentcircumcircle

Problem Statement

The line passing through vertex AA of triangle ABCABC and parallel to BCBC meets the circumcircle of ABCABC for the second time at point A1A_1. Points B1B_1 and C1C_1 are defined similarly. Prove that the perpendiculars from A1,B1,C1A_1, B_1, C_1 to BC,CA,ABBC, CA, AB respectively concur.
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