Question 78
Let $\triangle ABC$ be a triangle inscribed in a unit circle with center $O$. Let $I$ be the incenter of $\triangle ABC$, and let $D$ be the intersection of $BC$ and the angle bisector of $\angle BAC$. Suppose that the circumcircle of $\triangle ADO$ intersects $BC$ again at a point $E$ such that $E$ lies on $IO$. If $\cos A=\frac{12}{13}$, find the area of $\triangle ABC$.