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

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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 :

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴ OP ⊥ PQ

By Pythagoras theorem in ΔOPQ,

OQ2 = OP2 + PQ2
⇒ (12)2 = 52 + PQ2

⇒PQ2 = 144 - 25

⇒PQ2 = 119

⇒PQ = √119 cm

So, (D) is the right option.

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