Question

A chord of length $30$ cm is drawn at a distance of $8$ cm from the centre of a circle. The radius of the circle (in cm.) is

• A. $15$ cm
• B. $21$ cm
• C. $18$ cm
• D. $17$ cm

Answer 1

The correct option is D $17$ cm

Given-

$PR=30$ cm is the chord of a circle which is at a distance of $8$ cm from its center $O$.

To find out -

The radius of the circle $=?$

Solution-

We join $OP$.

Now $PQ=\frac{1}{2}PR=\frac{1}{2}\times 30$ cm $=15$ cm

Since the perpendicular from the centre of a circle to a chord bisects the latter.

So, in $\Delta OPQ$, by Pythagoras theorem, we have

$OP=\sqrt{{OQ}^2+{PQ}^2}=\sqrt{{15}^2+8^2}$ cm $=17$ cm