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.

By Pythagoras theorem:

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:

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