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angle chasing inside a 20-80-80 triangle, perpendicular, CN =1/2 BC

Source: 2002 Romania JBMO TST2 p3

May 16, 2020
geometryanglesAngle Chasingequal segments

Problem Statement

Let ABCABC be an isosceles triangle such that AB=ACAB = AC and ∠A=20o\angle A = 20^o. Let MM be the foot of the altitude from CC and let NN be a point on the side ACAC such that CN=12BCCN =\frac12 BC. Determine the measure of the angle AMNAMN.
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