Question

The radius of a circle with centre $P$ is $25$ cm and the length of the chord is $48$ cm. The distance of the chord from centre $P$ of the circle is

• A. $24$ cm
• B. $5$ cm
• C. $7$ cm
• D. $12$ cm

Answer 1

The correct option is C $7$ cm

Given, $AB=48$ cm is a chord of the circle with centre $P$ and radius$=r=25$ cm.

$PN$ is the perpendicular distance of $AB$ from $P.$

We know that a chord of a circle is bisected by the line which is the perpendicular distance of the chord from the centre of the given circle.

Therefore, $AN=BN=\frac{48}{2}$ cm $=24$ cm.

Now, in $\Delta PAN$, $\angle PNA$ is a right angle.

$\Delta PAN$ is a right one with hypotenuse as $PA.$

Therefore, Applying Pythagoras theorem, we get $PN=\sqrt{{PA}^2-{AN}^2}=\sqrt{{25}^2-{24}^2}cm=7cm.$