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IX=IY for I incenter if <BAC=60^o

Source: X - Mathematics Regional Olympiad of Mexico Northeast 2010 P3

September 17, 2022
geometryincenter

Problem Statement

In triangle ABCABC, ∠BAC=60o\angle BAC= 60^o. Angle bisector of ∠ABC\angle ABC meets side ACAC at XX and angle bisector of ∠BCA\angle BCA meets side ABAB at YY. Prove that if II is the incenter of triangle ABCABC, then IX=IYIX=IY.
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