Let AB and BC be two intersecting chords of circle w, with arc \(\widehat{ABC}\) being a minor arc. Suppose that the radius of the circle is 5, that BC =6, and that segment AD is bisected by segment BC. Suppose Further that AD the only chord starting at A which is bisected by line BC. It follows that the sine of the central angle of minor arc \(\widehat{AB}\) is a rational number. If this number is expressed as a fraction m/n in lowest terms, what is the product mn?

(第一届AIME1983 第十五题)