#### 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 OQ = 12 cm. Length PQ is :

(A) 12 cm.

(B) 13 cm

(C) 8.5 cm

(D) `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^{2 }+ PQ^{2 }= OQ^{2 }

5^{2} + PQ^{2 }=12^{2 }

PQ^{2 }=144 − 25

PQ = `sqrt119 `

Hence, the correct answer is (D).

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#### Reference Material

Solution for 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 OQ = 12 cm. Length PQ is : concept: Tangent to a Circle. For the course CBSE