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Problem 4

Source: 2nd European Mathematical Cup

December 16, 2013
geometrycircumcirclegeometry unsolved

Problem Statement

Given a triangle ABCABC let DD, EE, FF be orthogonal projections from AA, BB, CC to the opposite sides respectively. Let XX, YY, ZZ denote midpoints of ADAD, BEBE, CFCF respectively. Prove that perpendiculars from DD to YZYZ, from EE to XZXZ and from FF to XYXY are concurrent.
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