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RMO 2016 ,Q5

Source:

October 25, 2016
geometry

Problem Statement

Let ABCABC be a triangle , ADAD an altitude and AEAE a median . Assume B,D,E,CB,D,E,C lie in that order on the line BCBC . Suppose the incentre of triangle ABEABE lies on ADAD and he incentre of triangle ADCADC lies on AEAE . Find ,with proof ,the angles of triangle ABCABC .
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