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isosceles 20-80-80 , M in AC, AM/MC = 1/2, H projection of C on BM, <AHB?

Source: Sharygin Geometry Olympiad 2015 Final 8.3

August 1, 2018
geometryisoscelesangle

Problem Statement

In triangle ABCABC we have AB=BC,∠B=20oAB = BC, \angle B = 20^o. Point MM on ACAC is such that AM:MC=1:2AM : MC = 1 : 2, point HH is the projection of CC to BMBM. Find angle AHBAHB.
(M. Yevdokimov)
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