Question

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. 20
B. 15
C. 22
D. 27

Answer 1

Correct Answer - 1
The centers are `(10,0)` and `(-15,0)`
and the radii are `r_(1)=6` and `r_(2)=9`
Also, `d=25,r_(1)+r_(2) lt d`.

So, the circle are neither intersecting nor touching. Therefore,
`PQ= sqrt(d^(2)-(r_(1)+r_(2))^(2))`
`=sqrt(625-225)`
`=20`