Question

From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is
(a) 25
(b) $\sqrt{313}$
(c) 5
(d) 1

Answer 1

We know that the radius and tangent are perperpendular at their point of contact.
Now, in right triangle OPQ
By using Pythagoras theorem, we have
OQ² = OP² + PQ²
⇒ (13)² = OP² + (12)²
⇒ OP² = 169 − 144
⇒ OP² = 25
⇒OP = 5 cm
Hence, the correct answer is option (c).