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60, 30, 90 and + angles

Source: May Olympiad 2021 L2 #3

June 8, 2021
geometry

Problem Statement

Let ABCABC be a triangle and DD is a point inside of the triangle, such that ∠DBC=60∘\angle DBC=60^{\circ} and ∠DCB=∠DAB=30∘\angle DCB=\angle DAB=30^{\circ}. Let MM and NN be the midpoints of ACAC and BCBC, respectively. Prove that ∠DMN=90∘\angle DMN=90^{\circ}.
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