Question 38
Let $ABC$ be an isosceles triangle with $AC = BC$ and $\angle ACB \lt 60^\circ$. We denote the incenter and circumcenter by $I$ and $O$, respectively. The circumcircle of triangle $BIO$ intersects the leg $BC$ also at point $D \neq B$.
a. Prove that the lines $AC$ and $DI$ are parallel.
b. Prove that the lines $OD$ and $IB$ are mutually perpendicular.
a. Prove that the lines $AC$ and $DI$ are parallel.
b. Prove that the lines $OD$ and $IB$ are mutually perpendicular.