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प्रश्न
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 ______
पर्याय
60 cm2
65 cm2
30 cm2
32.5 cm2
उत्तर
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
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