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

Options

A. `60cm^(2)`
B. `65cm^(2)`
C. `30cm^(2)`
D. `32.5cm^(2)`

Answer

A

Explanation

Fistly, draw a circle of radius 5 cm having center 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.
`:'OQbotQP` [since, AP is a tangent line]
In right angled `DeltaPQO,` `OP^(2)=OQ^(2)+QP^(2)`
`rArr13^(2)=5^(2)+QP^(2)`
`rArrQP^(2)=169-25=144`
`rArrQP=12cm`
Now, area of `DeltaOQP=(1)/(2)xxQPxxQO`
`=(1)/(2)xx12xx5=30cm^(2)`
:. Area of quadrilateral `QORP=2DeltaOQP`
`=2xx30=60cm^(2)`