Theorem 12-2

Intersecting Tangents and Chords Theorem

Include Formula
short definition

Formula: If two chords in a circle intersect, the product of the lengths of one chord and its segments equals the product of the lengths of the other chord and its segments.

Short definition: When two chords within a circle intersect, the product of the lengths of each chord segment is equal.

The Intersecting Tangents and Chords Theorem, also known as Theorem 12-2, states that in a circle, if two chords intersect, the products of their segments are equal.

In formula form, if two chords AB and CD intersect at point P inside a circle, the following relationship holds true:

AP × PB = CP × PD

where AP and PB represent the segments of chord AB, and CP and PD represent the segments of chord CD.