Question

A chord of length $8cm$ is drawn at a distance of $3cm$ from the centre of a circle. Calculate the radius of the circle.

• A. $3$cm
• B. $5$cm
• C. $6$cm
• D. $8$cm

Answer 1

Answer: (B)

$5$cm

$LetA\text{circle with center O and a chord AB of length 8cm}$
$\text{A perpendicular from centre of the circle to chord divides the}$
$\text{chord in two equal parts}$
$\text{Let the perpendicular from centre meets the chord at point C}$
$\text{hence AC=CB=4}$
$OC=3$
$\sin ceOAC\text{is a right angle triangle}$
$\text{so using Pythagorean Theorem}$
$O{A}^2=A{C}^2+O{C}^2$
$\Rightarrow O{A}^2=4^2+3^2$
$\therefore OA=\sqrt{16+9}=\sqrt{25}=5cm$