Intersecting Chords

Products of segments of intersecting chords are equal

Intersecting Chords Theorem

If two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

Picture of product of intersecting chords rule

$ A \cdot B = C \cdot D $

Practice Problems

Problem 1

In the circle below, the chord segments have the following lengths: A= 6, C=3, D=4. Use the theorem for the product of chord segments to find the value of D.

Answer to problem
Problem 2

In the circle below, the chord segments have the following lengths: D = 8, C = 3, A = 6. Use the theorem for the product of chord segments to find the value of B.

A • B = C • D
A • B = 3 • 8
6 • B = 24
B = 24 ÷ 6
B = 4

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