Question 143
In triangle $ABC$, denote by $T_A, T_B, T_C$ the tangency points of the excircles of $\triangle ABC$ with sides $BC$, $AC$ and $AB$, respectively. Let $O$ be the center of the circumscribed circle of $\triangle ABC$, and $I$ the center of its inscribed circle. It is known that $OI \parallel AC$. Prove that $\angle T_A T_B T_C = 90^\circ - \frac{1}{2} \angle ABC$.
**Fig.29**
**Fig.29**