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Similar Triangles and tangents to the orthocenter

Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 2 grade 9

August 4, 2016
geometrysimilar trianglescircumcircle

Problem Statement

Let HH be the orthocenter of an acute-angled triangle ABCABC. Point XAX_A lying on the tangent at HH to the circumcircle of triangle BHCBHC is such that AH=AXAAH=AX_A and XA≠HX_A \not= H. Points XB,XCX_B,X_C are defined similarly. Prove that the triangle XAXBXCX_AX_BX_C and the orthotriangle of ABCABC are similar.
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