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angle chasing with equilaterals (2013 HOMC Senior Q7)

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July 18, 2019
Equilateral TriangleEquilateralgeometryAngle Chasing

Problem Statement

Let ABCABC be an equilateral triangle and a point M inside the triangle such that MA2=MB2+MC2MA^2 = MB^2 +MC^2. Draw an equilateral triangle ACDACD where D≠BD \ne B. Let the point NN inside △ACD\vartriangle ACD such that AMNAMN is an equilateral triangle. Determine ∠BMC\angle BMC.
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