Mock AIME 4 2006-2007 Problems/Problem 4

Problem

Points $A$ , $B$ , and $C$ are on the circumference of a unit circle so that the measure of $\widehat{AB}$ is $72^{\circ}$ , the measure of $\widehat{BC}$ is $36^{\circ}$ , and the measure of $\widehat{AC}$ is $108^\circ$ . The area of the triangular shape bounded by $\widehat{BC}$ and line segments $\overline{AB}$ and $\overline{AC}$ can be written in the form $\frac{m}{n} \cdot \pi$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .