MathDB
circumcenter lies on midline of other triangle (2019 Kyiv City MO Round2 11.3)

Source:

September 19, 2020
geometryCircumcentermidline

Problem Statement

The line ℓ\ell is perpendicular to the side ACAC of the acute triangle ABCABC and intersects this side at point KK, and the circumcribed circle △ABC\vartriangle ABC at points PP and TT (point P on the other side of line ACAC, as the vertex BB). Denote by P1P_1 and T1T_1 - the projections of the points PP and TT on line ABAB, with the vertices A,BA, B belong to the segment P1T1P_1T_1. Prove that the center of the circumscribed circle of the △P1KT1\vartriangle P_1KT_1 lies on a line containing the midline △ABC\vartriangle ABC, which is parallel to the side ACAC.
(Anton Trygub)
Back to ProblemsView on AoPS