## Proof of Formula Between Extended Chords

Theorem

The product of the lengths of chords of a circle with the extended chords that intersect outside a circle are equal.

Proof

Draw the chordsand

Angleis common to trianglesand

Anglesandare the same, since both are subtended by the pointsandon the circumference.

Hence anglesandare the same so that trianglesandare similar.

Hence