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TOT 218 1989 Spring S2 incenter wanted, <BMC = 90^o + 1/2 < BAC

Source:

March 7, 2021
geometryincenteranglesCircumcenter

Problem Statement

The point MM , inside △ABC\vartriangle ABC, satisfies the conditions that ∠BMC=90o+12∠BAC\angle BMC = 90^o +\frac12 \angle BAC and that the line AMAM contains the centre of the circumscribed circle of △BMC\vartriangle BMC. Prove that MM is the centre of the inscribed circle of △ABC\vartriangle ABC.
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