Question 15
The adjoining figure shows two intersecting chords in a circle, with $B$ on minor arc $AD.$ Suppose that the radius of the circle is $5,$ that $BC=6,$ and that $AD$ is bisected by $BC.$ Suppose further that $AD$ is the only chord starting at $A$ which is bisected by $BC.$ It follows that the sine of the minor arc $AB$ is a rational number. If this fraction is expressed as a fraction $\frac{m}{n}$ in lowest terms, what is the product $mn?$
