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M,N in AB,AC so that (ABC) bisects MN, <A=60^o

Source: Sharygin Geometry Olympiad 2016 Final Round problem 6 grade 8

July 22, 2018
geometrycircumcircleratio

Problem Statement

A triangle ABC with ∠A=60o\angle A = 60^o is given. Points MM and NN on ABAB and ACAC respectively are such that the circumcenter of ABCABC bisects segment MNMN. Find the ratio AN:MBAN:MB.
by E.Bakaev
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