Question

In a circle whose radius is $10$ inches, a chord is $6$ inches from the center. What is the length of the chord?

• A. $8$ inches
• B. $6$ inches
• C. $4$ inches
• D. $16$ inches

Answer 1

Answer: (D)

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