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Equal Angles With Midpoint Of AH

Source: Iran Third Round 2013 - Geometry Exam - Problem 4

September 6, 2013
geometrycircumcircletrigonometrygeometry unsolved

Problem Statement

In a triangle ABCABC with circumcircle (O)(O) suppose that AA-altitude cut (O)(O) at DD. Let altitude of B,CB,C cut AC,ABAC,AB at E,FE,F. HH is orthocenter and TT is midpoint of AHAH. Parallel line with EFEF passes through TT cut AB,ACAB,AC at X,YX,Y. Prove that ∠XDF=∠YDE\angle XDF = \angle YDE.
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