Question

What is the diameter of a circle, if a chord of length $24$ m is at a distance of $5$ m from the center of the circle?

• A. $13$ m
• B. $12$ m
• C. $26$ m
• D. $11$ m

Answer 1

The correct option is C $26$ m

Let $O$ be the center of the circle and $AB$ be a chord of length $24$ m.
From $O$, perpendicular $OP$ is drawn on $AB$ and $OA$ is joined.
Thus, $P$ is the midpoint of $AB$.
$AP=\frac{1}{2}AB=\frac{1}{2}\times 24=12$ m
$OP=5$ m
So, from the right angled $\Delta OAP$,
$O{A}^2=A{P}^2+O{P}^2={12}^2+5^2=169$
Squaring on both the sides we get,
$OA=13$ m
Hence, the radius of the circle $=13$ m.
Diameter $=2\times$ radius $=13\times 2=26$ m