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

• A. 7 cm
• B. 12 cm
• C. 15 cm
• D. 24.5 cm

Answer 1

The Correct Option is A

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