# 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.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 10

**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

**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.

**☛ Related Questions:**

- How many tangents can a circle have?
- Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
- Fill in the blanks:(i) A tangent to a circle intersects it in _____ point (s).(ii) A line intersecting a circle in two points is called a _____.(iii) A circle can have _____ parallel tangents at the most.(iv) The common point of a tangent to a circle and the circle is called _____.

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