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Question

Let C1 and C2 are circles defined by x2+y2−20x+64=0 and x2+y2+30x+144=0. The length of the shortest line segment PQ that is tangent to C1 at P and C2 at Q is

A
15
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B
18
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C
20
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D
24
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Solution

The correct option is C 20

C1=x2+y220x+64=0
C1=x2+y2+30x+144=0
C1:(10,0),r1=6\\ C2:(15,0),r2=9
C1C2=25,r1+r2=15
C1C2>r1+r2
m:n=9:6
R=(9×10156(15)2)=(60,0)
QS+PS=15292+10262=12+8=20

652334_126894_ans_6a7a5400163945639a7c21dc13060720.png

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