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Moldova JTST 2019 P11

Source:

April 19, 2019
geometrycircumcircle

Problem Statement

Let II be the center of inscribed circle of right triangle ΔABC\Delta ABC with ∠A=90\angle A = 90 and point MM is the midpoint of (BC)(BC).The bisector of ∠BAC\angle BAC intersects the circumcircle of ΔABC\Delta ABC in point WW.Point UU is situated on the line ABAB such that the lines ABAB and WUWU are perpendiculars.Point PP is situated on the line WUWU such that the lines PIPI and WUWU are perpendiculars.Prove that the line MPMP bisects the segment CICI.
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