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 ______.

Options

• 12 cm

• 13 cm

• 8.5 cm

• `sqrt119` cm

Answer 1

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 `bbunderline(sqrt119  cm)`.

Explanation:

Suppose there is a circle whose center is O.

In right ΔQPO,

According to Pythagoras theorem,

OQ² = OP² + PQ²

= PQ = `sqrt(OQ^2 - OP^2)`

= PQ = `sqrt(12^2 - 5^2)`

= PQ = `sqrt(144 - 25`

= PQ = `sqrt119` cm.