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double angle in a triangle given, equal segments wanted

Source: Mexican Mathematical Olympiad 2001 OMM P5

July 30, 2018
geometryequal segments

Problem Statement

ABCABC is a triangle with AB<ACAB < AC and ∠A=2∠C\angle A = 2 \angle C. DD is the point on ACAC such that CD=ABCD = AB. Let L be the line through BB parallel to ACAC. Let LL meet the external bisector of ∠A\angle A at MM and the line through CC parallel to ABAB at NN. Show that MD=NDMD = ND.
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