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angle bisector wanted, 135-30-15 triangle

Source: 2023 Chile NMO L2 P6

May 19, 2024
geometryangle bisector

Problem Statement

Let △ABC\vartriangle ABC be a triangle such that ∠ABC=30o\angle ABC = 30^o, ∠ACB=15o\angle ACB = 15^o. Let MM be midpoint of segment BCBC and point NN lies on segment MCMC, such that the length of NCNC is equal to length of ABAB. Proce that ANAN is the bisector of the angle ∠MAC\angle MAC. https://cdn.artofproblemsolving.com/attachments/2/7/4c554b53f03288ee69931fdd2c6fbd3e27ab13.png
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