Question

In the figure, 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

Options

• 30 cm

• 28 cm

• 32 cm

• 25 cm

Answer 1

32 cm

Explanation:

The tangent at any point of a circle is perpendicular to the radius at the point of contact.

∴ OT ⊥ PT

In right-angled triangle PTO,

OP² = OT² + PT²   ...(By Pythagoras Theorem)

⇒ OP² = (7)² + (24)²  ...(Given, radius, OT = 7 cm and PT = 24 cm)

⇒ OP² = 49 + 576

⇒ OP² = 625

⇒ OP = 25 cm

Hence, PR = OP + OR   ...(∵ OR = OT = Radii of circle)

= 25 + 7

= 32 cm