Question

Find the distance of the chord from the center. A chord of length $16$ m is drawn in a circle of diameter $20$ m.

• A. $3$ m
• B. $6$ m
• C. $9$ m
• D. $12$ m

Answer 1

The correct option is B $6$ m

Let $O$ be the center of the circle and $AB$ be a chord of length $16$ m.
From $O$, perpendicular $OP$ is drawn on $AB$ and $OA$ is joined.
Thus, $P$ is the midpoint of $AB$.
$AP=\frac{1}{2}AB=\frac{1}{2}\times 16=8$ m
$OP=?$ m
radius $=10$ m $=OA$
So, from the right angled $\Delta OAP$,
$O{A}^2=A{P}^2+O{P}^2$
${10}^2-8^2=O{P}^2$
$100-64=O{P}^2$
$36=O{P}^2$
Squaring on both the sides we get,
$OP=6$ m
Hence, distance of the chord from the center $=6$ m.