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If O is the centre of a circle of radius 5cm and at a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then, which of the following is the area of the quadrilateral PQOR?

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cm 2

32.5

cm 2

cm 2

cm 2

answer is A.

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Detailed Solution

Given that, OQ= 5cm, OR = 5cm, OP= 13cm and

∠ O Q P = ∠ O R P = 90 °

.
By Pythagoras theorem,
In triangle PQO,

P Q 2 + O Q 2 = O P 2

P Q 2 = O P 2 − O Q 2 ⇒ P Q 2 = 132 − 52 ⇒ P Q 2 = 169 − 25 ⇒ P Q 2 = 144

Simplifying,

⇒ P Q = 144 ⇒ P Q = 12 c m

We know that,

Area of a triangle = 12 × base × height

.
The area of the triangle OQP,

= 12 × P Q × O Q = 12 × 12 × 5 c m 2 = 30 c m 2

Then, the area of triangle ORP will also be

30 c m 2 .

The area of the quadrilateral PQOR= Area of triangle OQP + Area of triangle ORP.

= (30 + 30) c m 2 = 60 c m 2

Hence, the area of the quadrilateral

PQOR is 60 cm 2 .

Therefore, option 1 is correct.

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