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. Then find radius of the circle ?​

Answer 1

Answer:

let centre be O

so OQ is hypotenuse(opposite to 90degrees)

By Pythagoras theorem

OQ^2=base^2+24^2

625=base^2+576

base^2=49

base=7cm

radius of circle=7cm

Answer 2

Answer:

Explanation:

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 OQ=25cm

We have to find the radius  OP

Since QP is tangent

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

So, \angle OPQ =90  ∘

 So apply Pythagoras theorem to right triangle, OPQ;

{OP}^{2}={OQ}^{2}-{PQ}^2

{OP}^{2}={25}^{2}-{24}^{2}

= 625-576

 

{OP}^{2}=49cm

OP=\sqrt{49}OP=  

​ OP=7cm