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 chords
and
Angle
is common to triangles
and
Angles
and
are the same, since both are subtended by the points
and
on the circumference.
Hence angles
and
are the same so that trianglesandare similar.
Hence
