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Question

Let two circles touch each other externally and P is the point of intersection of there direct common tangents. If the direct common tangents from P touches the circles at A and B on same side and PA=AB=4, then the radius of smaller circle (in units) is 
  1. 2
  2. 2
  3. 22
  4. 4


Solution

The correct option is B 2

Let the radius of the small circle be r
As PAC1 and PBC2 are similar, so
PAPB=AC1BC244+4=rBC2BC2=2r
We know the length of direct common tangent is
AB=d2(r1r2)24=(3r)2(2rr)2r=2

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