The length of radius of a circel with centre O is 5 cm. P is a point at a distacne of 13 cm from the point O. PQ and PR are two tangensts from the point P to the circles, the area of the quadrilaterals PQOR is

Options

A. 60 sq-cm
B. 30 sq-cm
C. 120 sq-cm
D. 150 sq-cm

Explanation

The length of the radius of a circle with centre `O. therefore OQ =OR =5 cm.`
P is a point at a distance of 13 cm from the point `O. therefore OP=13 cm`
Now, PQ and PR are two tangents from P and OP and OR are radii passing through the point of contact.
`therefore OQ bot PQ and OR bot PR`
`therefore angle OQP =90^(@)and angle ORP =90^(@)`
i.e., `DeltaPOQand DeltaPOR` are both right-angled triangles.
`therefore Delta POQ =1/2 xx PQ xxOQ [because PQ =` base and OQ = height]
`=1/2 xx12xx5sq-cm.[because PQ =sqrt(OP^(2)-OQ^(2))=sqrt(13^(2) -5^(2))cm`
`=30 sq.cm =sqrt(169-25)cm =sqrt 144cm =12` cm.
Similarly, `DeltaPOR=1/2xxPRxxOR[because PR=` baseand height = OR]
`=1/2 xx12xx5 sq -cm [because PR=PQ =12 cm]=30sq-cm.`
`therefore` Ares of the quadrilateral `PQOR= DeltaPOQ+DeltaPOR=30 sq-cm+30 sq-cm=60sq-cm.`
`therefore` (a) is correct