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Intersecting Chord Theorem - IGCSE Maths Definition

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What is the intersecting chord theorem in IGCSE maths?

The Intersecting Chord Theorem states that if two chords of a circle intersect at a point inside the circle, the products of the lengths of the segments of each chord are equal.

  • For two chords, A B spaceand C D that meet at point P

    • A P colon P D identical to C P colon P B

    • Ratio of longer lengths (of chords) ≡ Ratio of shorter lengths (of chords)

  • This can also be written as A P cross times P B equals C P cross times P D

Diagram illustrating the intersecting chord theorem in a circle. Chords AB and CD intersect at P, forming segments with lengths a, b, c, d, where ab = cd.

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Reviewer: Amber

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Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

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