From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ______ - Mathematics

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From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ______ 

Options

  • 60 cm2

  • 65 cm2

  • 30 cm2

  • 32.5 cm2

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Solution

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is 60 cm2.

Explanation:

Firstly, draw a circle of radius 5 cm with centre O.

P is a point at a distance of 13 cm from O.

A pair of tangents PQ and PR are drawn.

Thus, quadrilateral PQOR is formed.

∵ OQ ⊥ QP  ...[Since, QP is a tangent line]

In right angled ∆PQO,

OP2 = OQ2 + QP2

⇒ 132 = 52 + QP2

⇒ QP2 = 169 – 25 = 144

⇒ QP = 12 cm

Now, area of ∆OQP

= `1/2 xx "QP" xx "QO"`

= `1/2 xx 12 xx 5`

= 30 cm2

∴ Area of quadrilateral PQOR

= 2 × ar ∆OQP

= 2 × 30

= 60 cm2

  Is there an error in this question or solution?
Chapter 9: Circles - Exercise 9.1 [Page 103]

APPEARS IN

NCERT Exemplar Mathematics Class 10
Chapter 9 Circles
Exercise 9.1 | Q 4 | Page 103

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