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Intersecting Chord Theorem


IntersectingChordTheorem

The intersecting chord theorem states that if chords AB and CD of a circle intersect at an interior point P, then

 PA·PB=PC·PD.

For unsigned lengths, the common product is the absolute value of the circle power of P. The corresponding result for an exterior point is stated using two secant lines. The product formula is distinct from the chord-chord angle formula for the angle between the chords.


See also

Chord, Chord-Chord Angle, Circle Power, Secant Line

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References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 81, 1989.

Cite this as:

Weisstein, Eric W. "Intersecting Chord Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntersectingChordTheorem.html

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