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incenter of BCD lies on circumcenter of ABD (2022 Novosibirsk Oral Geo Oly 9.4)

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September 3, 2023
geometryincentercircumcircle

Problem Statement

A point DD is marked on the side ACAC of triangle ABCABC. The circumscribed circle of triangle ABDABD passes through the center of the inscribed circle of triangle BCDBCD. Find ∠ACB\angle ACB if ∠ABC=40o\angle ABC = 40^o.
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