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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 :

  1. 12 cm

  2. 13 cm

  3. 8.5 cm

  4. 119\sqrt{119} cm.

Circles

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Answer

We know that,

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

From figure,

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 : NCERT Class 10 Mathematics CBSE Solutions.

PQ is the tangent.

So,

OP ⊥ PQ

In △OPQ,

By pythagoras theorem,

⇒ OQ2 = OP2 + PQ2

⇒ 122 = 52 + PQ2

⇒ 144 = 25 + PQ2

⇒ PQ2 = 144 - 25

⇒ PQ2 = 119

⇒ PQ = 119\sqrt{119} cm.

Hence, Option 4 is the correct option.

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