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Equilateral

Source: INMO 2001 Problem 5

October 10, 2005
geometrycircumcircletrigonometrytrig identitiesLaw of Sinesgeometry unsolved

Problem Statement

ABCABC is a triangle. MM is the midpoint of BCBC. ∠MAB=∠C\angle MAB = \angle C, and ∠MAC=15∘\angle MAC = 15^{\circ}. Show that ∠AMC\angle AMC is obtuse. If OO is the circumcenter of ADCADC, show that AODAOD is equilateral.
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