Problem

Source: Kyiv City MO 2022 Round 2, Problem 10.3

Tags: geometry, ratio



Let AHA,BHB,CHC be the altitudes of triangle ABC. Prove that if HBCAC=HCAAB, then the line symmetric to BC with respect to line HBHC is tangent to the circumscribed circle of triangle HBHCA. (Proposed by Mykhailo Bondarenko)