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Mixtilinear touchpoint is midpoint of side

Source: Sharygin Finals 2017, Problem 9.2

August 3, 2017
geometryratio

Problem Statement

Let II be the incenter of a triangle ABCABC, MM be the midpoint of ACAC, and WW be the midpoint of arc ABAB of the circumcircle not containing CC. It is known that ∠AIM=90∘\angle AIM = 90^\circ. Find the ratio CI:IWCI:IW.
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