Transverse common tangents are drawn from O to the two circles `C_1,C_2` with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles `C_1 and C_2` and chord of contacts of O w.r.t the circles `C_1 and C_2` respectively is

Options

A. 3 units
B. 6 units
C. 4 units
D. 5 units

Answer

C

Explanation

Let `r_(1) =2` and `r_(2) = 4`
Now, `(OP)/(OQ) = (r_(1))/(r_(2))`
`OP = (rr_(1))/(r_(1)+r_(2))`
`OQ = (rr_(1))/(r_(1)+r_(2))`
As triangles OAB and OCD are similar, we have
`(ar(DeltaOCD))/(ar(DeltaOAB)) =((OC)^(2))/((OA)^(2)) =(((rr_(2))/(r_(2)+r_(2))sin theta)/((rr_(1))/(r_(1)+r_(2))sintheta)) =(r_(1)^(2))/(r_(1)^(2)) =4`