The adjoining figure shows two intersecting chords in a circle, with B on minor arc A D. Suppose that the radius of the circle is 5 , that B C=6, and that A D is bisected by B C. Suppose further that A D is the only chord starting at A which is bisected by B C. It follows that the sine of the central angle of minor arc A B is a rational number. If this number is expressed as a fraction m / n in lowest terms, what is the product m n ?
