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Question

If two circles of radius 25 units and 16 units touch each other externally, then the radius of the circle which touches both of them externally and also their direct common tangent is


A
20 units
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B
40081 units
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C
412 units 
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D
92 units 
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Solution

The correct option is B 40081 units

We know that for two circle touching externally, length of direct common tangent
AB=d2(r1r2)2AB=2r1r2  ( d=r1+r2)AB=22516=40

Let radius of required circle be r
We know that,
AB=AP+PB40=225r+2r1640=18rr=(209)2=40081 units

Mathematics

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