Question

From a point q the length of the tangent to a circle is 24cm and the distance of q from the centre is 25cm the radius of the circle is

Answer 1

let's take centre point is o

then tangent is aq = 24

distance from q to centre is (oq) =25

radius of circle is ao=?

from pithogorus theoem is oq2 = ao2 + aq2

then (ao)2 = (oq)2 - (aq)2

(ao)2 = (25)2 - (24)2

(ao)2 = 625 - 576

(ao)2 = 49

(ao) =√49

ao = 7

radius of the circle is 7cm

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;

OP 2=OQ −PQ 2

OP 2 =25 2 −24 2

OP 2 =49cmOP= 49

OP=7cm

option A is the answer.