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 that
and
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 that
hence
or 
