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Let `C_1 and C_2` are circles defined by `x^2+y^2 -20x+64=0` and `x^2+y^2+30x +144=0`. The length of the shortest line segment PQ that is tangent to `C_1` at P and to `C_2` at Q is

A

`15`

B

`18`

C

`20`

D

`24`

Text Solution

Verified by Experts

The correct Answer is:
C

`r_(1)=t,r_(2)=9`
`r_(1)+r_(2)ltd` (dist between centres)
`implies` circle are seprated
`PQ=l=sqrt(d^(2)-(r_(1)+r_(2))^(2))=sqrt(625-225)=20`
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