there are two circles touching each other at one point. The radius of bigger circle is 4cm and smaller is 1cm. A small third circle is drawn which touches both the first two circles at one point each. A common tangent passes through all the three circles.Find the radius of this third cirlcle.

Answer 1

This problem is discussed at

http://mathworld.wolfram.com/TangentCircles.html

starting at equation (17), where we see that

1/√r = 1/√4 + 1/√1
1/√r = 1/2 + 1
1/√r = 3/2
r = 4/9