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.

$ N \cdot M = L \cdot M $

Picture of product of intersecting chords rule

Intersecting Chords Applet

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Drag Points To Start Demonstration

Practice Problems

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.

diagram chords segments

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

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