`C_(1) and C_(2)` are two concentric circles with centres at O. Their radii are 12 cm and 3 cm respectively. B and C are the points of contact of two tangents draw to `C_(2)` from a point A lying on the circle `C_(1)`. Then the area of the quadrilateral ABOC is-

Options

A. `(9 sqrt(15))/(2)` वर्ग सेमी
B. `12 sqrt(15)` वर्ग सेमी
C. `9 sqrt(15)` वर्ग सेमी
D. `6sqrt(15)` वर्ग सेमी

Answer

C

Explanation

`OB bot AB`
`DeltaAOB` में,

`AB= sqrt(OA^(2)-OB^(2))`
`= sqrt(12^(2)-3^(2))= sqrt(144*-9)= sqrt(135)`
`rArr AB= 3 sqrt(15)`
`Delta AOB` का क्षे0 `=(1)/(2)AB.OB`
`=(1)/(2)*3 sqrt(15)*3= ((9 sqrt(15))/(2)) cm^(2)`
`DeltaAOB=DeltaAOC`
`:. DeltaABOC` का क्षे `=2DeltaAOB`
`=2xx (9 sqrt(15))/(2)=9 sqrt(15) cm^(2)`