Hey I've got a problem I'm trying to do to brush up on my skills (exam season...):

Consider a circle inscribed in a square with each side of the square having a length of 1 unit. Now at each the four corners, additional circles are constructed that are externally tangent to the original circle and tangent to the square. This is continued forever; what is the total area ofallcircles?

I think I can do the part of computing the by making the formula for the series fairly easy. Obviously, the first (and biggest) circle has a radius of 0.5.

My problem is: how do I find the size/radius/area of thenexttriangle(s) - the ones in the corner?

Thanks, any help is greatly appreciated!