MathDB
Equal ratio implies tangency

Source: Kyiv City MO 2022 Round 2, Problem 10.3

January 30, 2022
geometryratio

Problem Statement

Let AHA,BHB,CHCAH_A, BH_B, CH_C be the altitudes of triangle ABCABC. Prove that if HBCAC=HCAAB\frac{H_BC}{AC} = \frac{H_CA}{AB}, then the line symmetric to BCBC with respect to line HBHCH_BH_C is tangent to the circumscribed circle of triangle HBHCAH_BH_CA.
(Proposed by Mykhailo Bondarenko)
Back to ProblemsView on AoPS