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anglechasing with incenter, 60^o wanted (Singapore Junior 2006)

Source:

July 10, 2019
geometryAngle Chasingangle bisectorincenter

Problem Statement

In △ABC\vartriangle ABC, the bisector of ∠B\angle B meets ACAC at DD and the bisector of ∠C\angle C meets ABAB at EE. These bisectors intersect at OO and OD=OEOD = OE. If AD≠AEAD \ne AE, prove that ∠A=60o\angle A = 60^o.
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