A circle has radius $10\text{ cm}$. The distance of a chord from the centre is $6\text{ cm}$. Find the length of the chord.

Step-by-step solution

1. Draw the radius to the midpoint $M$ of the chord; $OM$ is perpendicular to the chord.
2. In right triangle $OMC$, $OC=10\text{ cm}$ (radius) and $OM=6\text{ cm}$ (given).
3. Apply Pythagoras: $(\frac{c}{2}{)}^2=O{C}^2-O{M}^2=10^2-6^2=100-36=64$.
4. Hence $\frac{c}{2}=8\text{ cm}$, giving chord length $c=16\text{ cm}$.

Concept tested: Chord length from distance to centre

Published 20 August 2026 · Last updated 16 September 2026 · How this solution was prepared and checked