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Intersection lies on AM

Source: Junior Olympiad of Malaysia Shortlist 2015 G2

July 17, 2015
geometry

Problem Statement

Let ABC ABC be a triangle, and let MM be midpoint of BCBC. Let Ib I_b and Ic I_c be incenters of AMB AMB and AMC AMC . Prove that the second intersection of circumcircles of ABIb ABI_b and ACIc ACI_c distinct from AA lies on line AMAM.
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