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chords product segment

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 example with numbers

$ N \cdot O = L \cdot M $

Picture of product of intersecting chords rule

$ 2 \cdot 6 = 3 \cdot 4 $

Picture of product of intersecting chords example with numbers

Intersecting Chords Applet

. = .
* = *
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Drag Points To Start Demonstration

Practice Problems

Problem 3

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.

diagram chords segments

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

Back to Circles