Two chords $AB$ and $CD$ of a circle intersect at point $E$ inside the circle. If $AE=3\text{ cm}$, $EB=5\text{ cm}$ and $CE=2\text{ cm}$, find $ED$.

Step-by-step solution

1. Apply the intersecting chords theorem: $AE\times EB=CE\times ED$.
2. Substitute the known lengths: $3\times 5=2\times ED$.
3. Solve for $ED$: $ED=\frac{3\times 5}{2}=\frac{15}{2}=7.5\text{ cm}$.

Concept tested: Intersecting chords theorem

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

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