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perpendicular wanted, circle with diameter AP, P random, orthocenter related

Source: 2015 Saudi Arabia IMO TST I p2

July 24, 2020
geometryperpendicularcirclrorthocenter

Problem Statement

Let ABCABC be a triangle with orthocenter HH. Let PP be any point of the plane of the triangle. Let Ω\Omega be the circle with the diameter APAP . The circle Ω\Omega cuts CACA and ABAB again at EE and FF , respectively. The line PHPH cuts Ω\Omega again at GG. The tangent lines to Ω\Omega at E,FE, F intersect at TT. Let MM be the midpoint of BCBC and LL be the point on MGMG such that ALAL and MTMT are parallel. Prove that LALA and LHLH are orthogonal.
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