Find the length of a chord of a circle whose radius is $13\text{ cm}$ and whose distance from the centre is $5\text{ cm}$.

Step-by-step solution

1. Join the centre $O$ to the midpoint $M$ of the chord; $OM$ is perpendicular to the chord.
2. In right triangle $OMA$, $OM=5\text{ cm}$ and $OA=13\text{ cm}$ (radius).
3. Apply Pythagoras: $AM=\sqrt{O{A}^2-O{M}^2}=\sqrt{13^2-5^2}=\sqrt{144}=12\text{ cm}$.
4. The chord length $AB=2\times AM=2\times 12=24\text{ cm}$.

Concept tested: Chord length from distance

Published 22 August 2026 · How this solution was prepared and checked

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