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


(SOLVE THE ALL QUEST PLIS)​

Answer 1

✎ Solution

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