#### Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

12 cm.

13 cm

8.5 cm

`sqrt119` cm test

#### Solution

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

∴OP ⊥ PQ

By applying Pythagoras theorem in ΔOPQ,

∴OP^{2 }+ PQ^{2 }= OQ^{2 }

5^{2} + PQ^{2 }=12^{2 }

PQ^{2 }=144 − 25

PQ = `sqrt119 `

Hence, the correct answer is `sqrt119` cm test.

Is there an error in this question or solution?

Solution A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is : Concept: Tangent to a Circle.