MathDB
Incenter coincides with orthocenter

Source: Russian TST 2015, Day 10 P3 (Group NG), P4 (Groups A & B)

April 21, 2023
geometryincenterorthocenter

Problem Statement

The triangle ABCABC is given. Let A′A' be the midpoint of the side BCBC, BcB_c{} be the projection of BB{} onto the bisector of the angle ACBACB{} and CbC_b be the projection of the point CC{} onto the bisector of the angle ABCABC. Let A0A_0 be the center of the circle passing through A′,Bc,CbA', B_c, C_b. The points B0B_0 and C0C_0 are defined similarly. Prove that the incenter of the triangle ABCABC coincides with the orthocenter of the triangle A0B0C0A_0B_0C_0.
Back to ProblemsView on AoPS