MathDB
Cute geometry

Source: Caucasus MO 2023, senior, day 2, P8

March 12, 2023
geometry

Problem Statement

Let ABCABC be an acute-angled triangle, and let AA1,BB1,CC1AA_1, BB_1, CC_1 be its altitudes. Points A′,B′,C′A', B', C' are chosen on the segments AA1,BB1,CC1AA_1, BB_1, CC_1, respectively, so that ∠BA′C=∠AC′B=∠CB′A=90o\angle BA'C = \angle AC'B = \angle CB'A = 90^{o}. Let segments AC′AC' and CA′CA' intersect at B"B"; points A",C"A", C" are defined similarly. Prove that hexagon A′B"C′A"B′C"A'B"C'A"B'C" is circumscribed.
Back to ProblemsView on AoPS