Question

A chord of length $16$ cm is drawn in a circle at a distance of $15$ cm from its center. Find the radius of the circle.

• A. $12$ cm
• B. $15$ cm
• C. $17$ cm
• D. $34$ cm

Answer 1

The correct option is C $17$ cm

Let $AB$ be the chord of length $16$ cm

Given that distance from centre to the chord $AB$ is $OC=15$ cm

$OC\perp AB$ and $AC=CB$ [Since perpendicular drawn from centre of the circle bisects the chord]

$\therefore AC=CB=8$ cm

In right $\Delta OCA$,

$O{A}^2=A{C}^2+O{C}^2$

$O{A}^2=8^2+{15}^2$

$O{A}^2=64+225$

$O{A}^2=289$

$OA=17$ cm

Hence, the radius of the circle is $17$ cm.