MathDB
Tangency in nice configuration

Source: Serbia 2018 TST day 2 p5

May 28, 2018
geometryInversion

Problem Statement

Let HH be the orthocenter of ABCABC ,AB≠ACAB\neq AC ,and let FF be a point on circumcircle of ABCABC such that ∠AFH=90∘\angle AFH=90^{\circ} .KK is the symmetric point of HH wrt BB .Let PP be a point such that ∠PHB=∠PBC=90∘\angle PHB=\angle PBC=90^{\circ} ,and QQ is the foot of BB to CPCP .Prove that HQHQ is tangent to tge circumcircle of FHKFHK .
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