Problem

Source: 2002 Romania JBMO TST2 p3

Tags: geometry, angles, Angle Chasing, equal segments



Let $ABC$ be an isosceles triangle such that $AB = AC$ and $\angle A = 20^o$. Let $M$ be the foot of the altitude from $C$ and let $N$ be a point on the side $AC$ such that $CN =\frac12 BC$. Determine the measure of the angle $AMN$.