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Two circles of radii a and b (a < b) tou...

Two circles of radii a and b (a < b) touch externally. Length of the direct common tangent from the point of intersection of the direct common tangents to the smaller circle is

Text Solution

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`/_ ABM~~/_PQM` (AAA)
`(BM)/(QM)=(AB)/(PQ)=b/a`
`(BQ+QM)/QM=b/a` -(1)
AX=AB-XB
=b-a
In `/_AXP`
BQ=PX=`sqrt(AP^2-AX^2)`
=`sqrt((a+b)^2-(b-a)^2)`
...
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