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equal segments staring with an acure triangle, <A=45^o, O,H

Source: Iranian Geometry Olympiad 2018 IGO Advanced p2

September 19, 2018
geometryequal segmentsacute triangleCircumcenterorthocenter

Problem Statement

In acute triangle ABC,∠A=45oABC, \angle A = 45^o. Points O,HO,H are the circumcenter and the orthocenter of ABCABC, respectively. DD is the foot of altitude from BB. Point XX is the midpoint of arc AHAH of the circumcircle of triangle ADHADH that contains DD. Prove that DX=DODX = DO.
Proposed by Fatemeh Sajadi
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