Question

Find the radius of a circle, if a chord of length $8$ m is at a distance of $3$ m from the centre of the circle.

• A. $1$ m
• B. $2$ m
• C. $4$ m
• D. $5$ m

Answer 1

The correct option is D $5$ m

Let $O$ be the center of the circle and $AB$ be a chord of length $8$ m.
From $O$, perpendicular $OP$ is drawn on $AB$ and $OA$ is joined.
Thus, $P$ is the midpoint of $AB$.
$AP=\frac{1}{2}AB=\frac{1}{2}\times 8=4$ m
$OP=3$ m
So, from the right angled $\Delta OAP$,
$O{A}^2=A{P}^2+O{P}^2=4^2+3^2=25$
Squaring on both the sides we get,
$OA=5$ m
Hence, the radius of the circle $=5$ m.