Question

A chord AB of a circle whose centre is O, is bisected at E by a diameter CD. OC= OD = 15cm and OE = 9 cm. Find the length of AB.

• A. 12 cm
• B. 18 cm
• C. 24 cm
• D. 30 cm

Answer 1

The correct option is C 24 cm

Given, OE = 9 cm and OA = 15 cm.
We know that the segment joining the centre of a circle and the midpoint of its chord is perpendicular to the chord.
Therefore, $\angle OEA={90}^o$.
Applying Pythagoras' theorem to $△OAE$,
$A{E}^2=O{A}^2-O{E}^2$
$A{E}^2={15}^2-9^2$
$A{E}^2=225-81=144$
$\Rightarrow AE=12\text{cm}$
Chord AB is bisected by the diameter CD(given).
$\therefore AB=2\times 12=24\text{cm}$