Circle

Let C1 and C2 be circles defined by x^2－20x+y^2+64=0 and (x+15)^2+y^2=81
respectively. What is the length of the shortest line segment PQ that istangent to C1
at P and to C2 at Q?
Sol
x^2－20x+y^2+64=0
(x－20x+100)+y^2=100－64
(x－10)^2+y^2=36
(1) PQ為外公切線
PQ^2+(9－6)^2=25^2
PQ^2=616
PQ=2√154
(2) PQ為內公切線
PQ^2+(6+9)^2=25^2
PQ^2=400
PQ=20
So
Thelength of the shortest line segment PQ=20