This is another nice puzzle from the Scottish Mathematical Council (SMC) Senior Mathematical Challenge of 2008.

“The triangle ABC is inscribed in a circle of radius 1. Show that the length of the side AB is given by 2 sin c°, where c° is the size of the interior angle of the triangle at C.”

The diagram shows the case where C is on the same side of the chord AB as the center of the circle.  There is a second case to consider where C is on the other side of the chord from the center.

See the Circle Chord Problem