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<IMB=15^o wanted, incenter in 90-60-30 Puerto Rico TST 2021.2

Source:

September 22, 2021
geometryincenteranglesright triangle

Problem Statement

Let ABCABC be a right triangle with right angle at B B and ∠C=30o\angle C=30^o. If MM is midpoint of the hypotenuse and II the incenter of the triangle, show that ∠IMB=15o \angle IMB=15^o.
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