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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 : - Mathematics

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MCQ

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 test

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Solution

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

∴OP ⊥ PQ

By applying Pythagoras theorem in ΔOPQ,

∴OP+ PQ= OQ

52 + PQ=12

PQ=144 − 25

PQ = `sqrt119 `

Hence, the correct answer is `sqrt119` cm test.

Concept: Tangent to a Circle
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APPEARS IN

NCERT Class 10 Maths
Chapter 10 Circles
Exercise 10.1 | Q 3 | Page 209
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