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tangent wanted, isosceles, 2AC = AB + BC, incenter (2018 Kyiv City MO 11.4)

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September 12, 2020
geometryincentertangentisosceles

Problem Statement

Given an isosceles ABCABC, which has 2AC=AB+BC2AC = AB + BC. Denote II the center of the inscribed circle, KK the midpoint of the arc ABCABC of the circumscribed circle. Let TT be such a point on the line ACAC that ∠TIB=90∘\angle TIB = 90 {} ^ \circ. Prove that the line TBTB touches the circumscribed circle ΔKBI\Delta KBI.
(Anton Trygub)
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