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 PQ=12 cm. Find length of OQ​

Answer 1

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

• OP ⊥ PQ

Using Pythagoras theorem,

In triangle ΔOPQ we get,

→ OQ² = OP² + PQ²

→ OQ² = 5² + 12²

→ OQ² = 25 + 144

→ OQ² = 169

→ OQ = 13

Hence,

The length of the line OQ is 13 cm.