Question

In Fig, on a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle, then the length of PR is

(a) 30 cm (b) 28 cm (c) 32 cm (d) 25 cm

Answer 1

Correct option is (c) 32 cm

We know that,

Radius to a tangent is perpendicular at the point of contact

∴ In right ΔOTP,

By Pythagoras theorem

(OP)² = (OT)² + (PT)²

= (7)² + (24)²

= 49 + 576

= 625

∴ OP = 25 cm

Now,

PR = OP + OR 

= 25 + 7 

= 32cm

Answer 2

The correct option is (c) 32 cm.

In ΔPOT, 

(OP)² = (OT)² + (PT)²

OP² = (7)² + (24)²

OP² = (25)² 

OP = 25 cm 

PR = OP + OR 

= 25 + 7 

= 32 cm