MathDB
Cool geometry but easy)

Source: Ukrainian TST for IMO 2020, p3 1 round

January 4, 2021
geometrycircumcircleTangent LineAngle Chasingtrigonometrygeometry unsolved

Problem Statement

Altitudes AH1AH1 and BH2BH2 of acute triangle ABCABC intersect at HH. Let w1w1 be the circle that goes through H2H2 and touches the line BCBC at H1H1, and let w2w2 be the circle that goes through H1H1 and touches the line ACAC at H2H2. Prove, that the intersection point of two other tangent lines BXBX and AYAY( XX and YY are different from H1H1 and H2H2) to circles w1w1 and w2w2 respectively, lies on the circumcircle of triangle HXYHXY. Proposed by Danilo Khilko
Back to ProblemsView on AoPS