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find angles in triangle with A=60^o

Source: IGO 2015 Elementary 2

July 22, 2018

geometryElementaryangles

Problem Statement

Let

ABC

be a triangle with

\angle A = 60^o

. The points

M,N,K

lie on

BC,AC,AB

respectively such that

\angle C

. If

AN = 2AK

, find the values of

\angle B

and

\angle C

.
by Mahdi Etesami Fard

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