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Angle in triangle

Source: Singapore Mathematical Olympiad 2006 Problem 1

July 7, 2006
geometry proposedgeometry

Problem Statement

In the triangle ABC,∠A=π3,D,MABC,\angle A=\frac{\pi}{3},D,M are points on the line ACAC and E,NE,N are points on the line ABAB such that DNDN and EMEM are the perpendicular bisectors of ACAC and ABAB respectively. Let LL be the midpoint of MNMN. Prove that ∠EDL=∠ELD\angle EDL=\angle ELD
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