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

Answer:

(a)7 cm is the correct answer.

Answer 2

Answer:

Let QP be the tangent, such that, Point of contact is P.

Length of the tangent to a circle = 24cm

$$PQ=24cm$$

Let O be the centre of the circle.

OQ=25cm

We have to find the radius OP

Since QP is tangent

OP perpendicular to QP (Since, Tangent is Perpendicular to Radius at the point of contact)

So, ∠OPQ=90°

So apply Pythogoras theorem to right triangle, OPQ;

OP²=OQ²−PQ²

OP²=25² −24²

OP²=49cm

OP= √49

OP=7cm

option A is the answer.