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Question

If C1 and C2 are circles whose equations are x2+y2−20x+64=0 and x2+y2+30x+144=0, then the length of the shortest line segment PQ that is tangent to C1 at P and to C2 at Q is

A
15 units
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B
18 units
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C
20 units
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D
24 units
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Solution

The correct option is C 20 units
Given circles are
x2+y220x+64=0 and x2+y2+30x+144=0
The centre and radius are
C1=(10,0), r1=6C2=(15,0), r2=9
C1C2=d=25

The transverse common tangent is the shortest common tangent, so the required length
=d2(r1+r2)2=(25)2(9+6)2=400=20 units

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