Question

From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is 

 

 

Options

• A. 25

• B. `sqrt313`

• C. 5

• D. 1

Answer 1

The given information can be represented diagrammatically as follows:

Let O be the centre of the circle.

Given: PQ = 12 cm and OQ = 13 cm.

To find: Radius of the circle

PQ is a tangent drawn from the external point Q to the circle.

∠ OPQ = 90° (Radius is perpendicular to the tangent at the point of contact)

On applying Pythagoras theorem in ΔOPQ, we obtain:

OQ² = OP² + PQ²

∴ OP² = OQ² − PQ²

⇒ OP² = (13 cm)² − (12 cm)²

⇒ OP² = 169cm² − 144 cm²

⇒ OP² = 25 cm²

⇒ OP = 5 cm

Thus, the radius of circle is 5 cm.

Hence, the correct answer is C