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incenters of half the triangle

Source: KJMO 2018 p3

July 26, 2019
geometryincenter

Problem Statement

Let there be a scalene triangle ABCABC, and denote MM by the midpoint of BCBC. The perpendicular bisector of BCBC meets the circumcircle of ABCABC at point PP, on the same side with AA with respect to BCBC. Let the incenters of ABMABM and AMCAMC be I,JI,J, respectively. Let ∠BAC=α\angle BAC=\alpha, ∠ABC=β\angle ABC=\beta, ∠BCA=γ\angle BCA=\gamma. Find ∠IPJ\angle IPJ.
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