Question

A chord of a circle of radius $10$ cm subtends a right angle at its centre. The length of the chord (in cm) is

• A. $5\sqrt{2}$
• B. $10\sqrt{2}$
• C. $\frac{5}{\sqrt{2}}$
• D. $10\sqrt{3}$

Answer 1

The correct option is B $10\sqrt{2}$

Given in $\Delta AOC,OA=10$ cm, $OB=10$ cm and $\angle AOB={90}^0$

Using Pythagorus theorem in $\Delta AOB$ we can get $AB$

$AB=\sqrt{{OA}^2+{OB}^2}=\sqrt{{10}^2+{10}^2}=10\sqrt{2}$ cm.

Hence, length of the chord $AB$ is $10\sqrt{2}$ cm.