CK12 - Geometry

Segmentsof Secants

TheoremIf two secantsare drawnfrom a commonpointoutsidea circleand the segmentsare labeledas
below, then the segmentsof the secantssatisfythe followingrelationship:

This meansthat the productof the outsidesegmentof one secantand its wholelengthequalsthe product
of the outsidesegmentof the othersecantand its wholelength.

Proof

We connectpoints and and points and to make and.

Sameangle

Inscribedanglesinterceptingthe samearc

Therefore, by the AA similaritypostulate.

In similartrianglesthe ratiosof correspondingsidesare equal.