Question 179
A triangle $AB\Gamma$ is given with $AB \lt A\Gamma$. Let $I$ be the point of intersection of its bisectors. Bisector $A\Delta$ meets the circumcircle $C$ of the triangle $BI\Gamma$ at the point $N$ with $N \neq I$.
(i) Determine the angles of the triangle $B\Gamma N$ with respect to the angles of the triangle $AB\Gamma$,
(ii) the center of the circle $C$.
(i) Determine the angles of the triangle $B\Gamma N$ with respect to the angles of the triangle $AB\Gamma$,
(ii) the center of the circle $C$.