Mathematics Question on Number of Tangents from a Point on a Circle

Question

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

Answer 1

Solution

A circle with tangent PQ is 24 cm
Let $O$ be the centre of the circle
Given that,
$OQ = 25$ cm and $PQ = 24$ cm
As the radius is perpendicular to the tangent at the point of contact,
Therefore, $OP ⊥ PQ$
Applying Pythagoras theorem in $\text {ΔOPQ}$ , we obtain
$OP^2 + PQ^2 = OQ^2$
$OP^2 + 24^2 = 25^2$
$OP^2 = 625 - 576$
$OP^2 = 49$
$OP = 7$
Therefore, the radius of the circle is $7$ cm.

Hence, the correct option is (A): $7$ cm