Question

In 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 length OP = ?

(a) 30 cm 

(b) 28 cm 

(c) 25 cm 

(d) 18 cm

Answer 1

Correct answer is (c) 25 cm

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

∴ OT ⊥ PT

From right – angled triangle PTO,

∴ OP² = OT² + PT²     [Using Pythagoras' theorem]

\(\Rightarrow\) OP² = (7)² + (24)²

\(\Rightarrow\) OP² = 49 + 576

\(\Rightarrow\) OP² = 625

\(\Rightarrow\) OP = \(\sqrt{625}\)

\(\Rightarrow\) OP = 25 cm