# 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:

(A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm

**Solution:**

Given: Radius OP = 5 cm, OQ = 12 cm

We have to find the length of the tangent PQ.

ΔOPQ is a right-angle triangle according to Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

OQ² = OP² + PQ²

12² = 5² + PQ²

144 = 25 + PQ²

PQ² = 119

PQ = √119

Thus, the length of PQ is √119 cm.

**Video 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: (A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm

### NCERT Solutions Class 10 Maths Chapter 10 Exercise 10.1 Question 3 - Chapter 10 Exercise 10.1 Question 3:

**Summary:**

For a tangent PQ at a point P of a circle of radius 5 cm which meets a line through the centre O at a point Q so that OQ = 12 cm, the length of the tangent PQ is √119 cm.