Two chords $A B$ and $C D$ of a circle intersect at point $E$ inside the circle. If $A E = 4 cm$ , $E B = 6 cm$ , $C E = 3 cm$ and the radius of the circle is $10 cm$ , find the length of $E D$ .

hard 3 marks Class 10 · Mathematics · Circles

Answer

cm

The correct answer is 8 $cm$ — Solve for $E D$ : $E D = \frac{24}{3} = 8 cm$ .

Step-by-step solution

For intersecting chords, the intersecting chords theorem states $A E \times E B = C E \times E D$ .
Substitute the known lengths: $(4 cm) (6 cm) = (3 cm) (E D)$ .
Compute the left side: $4 \times 6 = 24$ cm $^{2}$ .
Solve for $E D$ : $E D = \frac{24}{3} = 8 cm$ .

Common mistake: Mixing up the order of the segments or forgetting to divide correctly to isolate

E D

Concept tested: Intersecting chords theorem

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