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) √119 cm

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Answer 1

Answer:

Answer is √119 cm

Step-by-step explanation:

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

therefore, OP perpendicular to PQ

By applying Pythagoras in OPQ

(OP)²+(PQ)²=(OQ)²

=> (5)²+(PQ)²=(12)²

=> (PQ)²=144-25

PQ=√119 cm

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Answer 2

ANSWER:-

(D) √119 cm

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Step by step explain:-

In the above figure, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ.

And so, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get,

Formula:-

$\mathtt{OQ {}^{2} = OP {}^{2} + PQ {}^{2} }$

$\mathtt{12 {}^{2} = {5}^{2} + PQ {}^{2} }$

$\mathtt{PQ {}^{2} = 144 - 25}$

$\mathtt{PQ {}^{2} = 119}$

$\mathtt\red{PQ = \sqrt{119}cm }$

So, option D.√119 cm is the length of PQ.