Let $\vartriangle ABC$ be a triangle in which $\angle ACB = 40^o$ and $\angle BAC = 60^o$ . Let $D$ be a point inside the segment $BC$ such that $CD =\frac{AB}{2}$ and let $M$ be the midpoint of the segment $AC$. How much is the angle $\angle CMD$ in degrees?
Problem
Source: Girls in Mathematics Tournament 2021 p2 (Brazil) / Torneio Meninas na Matematica (TM^2) / Brazil EGMO TST 2022 #1
Tags: geometry, angles