MathDB

2019.10.3

Part of Kyiv City MO Seniors Round2 2010+ geometry

Problems(1)

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

Source:

9/18/2020
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)
geometryexcentersexcenterangles