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Transverse common tangents are drawn fro...

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

A

3 units

B

6 units

C

4 units

D

5 units

Text Solution

Verified by Experts

The correct Answer is:
C

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`
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