Proof of Formula Between Intersecting Chords

For the chords drawn in the circle below,

To prove it complete the triangles and draw an extra chord from A to D and an extra chord from B to C as shown below.

From the Sine Rule for triangle ABO,and for triangle ODB,so thatand

C and D are equal since both are subtended from the same chord, AB and A and B are also equal since both are subtended from the same chord CD, so thathenceor