MathDB
(MNP) cuts triangle ABC and froms equilateral - 2003 Cuba MO 2.3

Source:

September 15, 2024
geometryEquilateral

Problem Statement

Let ABCABC be an acute triangle and TT be a point interior to this triangle. that ∠ATB=∠BTC=∠CTA\angle ATB = \angle BTC = \angle CTA. Let M,NM,N and PP be the feet of the perpendiculars from TT to BCBC, CACA and ABAB respectively. Prove that if the circle circumscribed around △MNP\vartriangle MNP cuts again the sides BC BC, CACA and ABAB in M1M_1, N1N_1, P1P_1 respectively, then the △M1N1P1\vartriangle M_1N_1P_1 It is equilateral.
Back to ProblemsView on AoPS