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<T_A T_B T_C= 90^o - 1/2 <ABC if OI//AC (2019 Kyiv City MO Round2 10.3)

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September 18, 2020
geometryexcentersexcenterangles

Problem Statement

Denote in the triangle ABCABC by TA,TB,TCT_A,T_B,T_C the touch points of the exscribed circles of △ABC\vartriangle ABC, tangent to sides BC,ACBC, AC and ABAB respectively. Let OO be the center of the circumcircle of △ABC\vartriangle ABC, and II is the center of it's inscribed circle. It is known that OI∥ACOI\parallel AC. Prove that ∠TATBTC=90o−12∠ABC\angle T_A T_B T_C= 90^o - \frac12 \angle ABC.
(Anton Trygub)
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