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collinear midpoints

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P16

August 1, 2018
geometrycollinearmidpoints

Problem Statement

Given a triangle ABCABC and an arbitrary point DD.The lines passing through DD and perpendicular to segments DA,DB,DCDA, DB, DC meet lines BC,AC,ABBC, AC, AB at points A1,B1,C1A_1, B_1, C_1 respectively. Prove that the midpoints of segments AA1,BB1,CC1AA_1, BB_1, CC_1 are collinear.
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