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<IMA=<INB wanted, incenter, midpoint and arc midpoint related

Source: 2017 Croatia MO p3

August 3, 2020
geometryincenterarc midpointequal angles

Problem Statement

In triangle ABCABC, ∣AB∣<∣BC∣|AB| <|BC| holds. Point II is the center of the circle inscribed in that triangle. Let MM be the midpoint of the side ACAC, and NN be the midpoint of the arc ACAC of the circumcircle of that triangle containing point BB. Prove that ∠IMA=∠INB\angle IMA = \angle INB.
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