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ID =IE if <ACB=60^o, 2 angle bisectors and incenter

Source: 2022 Chile National Olympiad level 2 p2

October 22, 2022
equal segmentsgeometryincenter

Problem Statement

Let ABCABC be a triangle such that ∠CAB=60o\angle CAB = 60^o. Consider D,ED, E points on sides ACAC and ABAB respectively such that BDBD bisects angle ∠ABC\angle ABC , CECE bisects angle ∠BCA\angle BCA and let II be the intersection of them. Prove that ∣ID∣=∣IE∣|ID| =|IE|.
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