complicated?

Question

consider two concentric circles with centre at C and a third circle with its centre on the outer of the two concentric circles and touching but not intersecting the inner circle.The annulus with center C has inner radius r & outer radius 1.As r increases the circle with center O contracts & remains tangent to the inner circle. If A(r) is the area of the annulus & a(r) is the area of the circular region with center o then lim r(tends to 1) A(r)/a(r)= ??????

Answer 1

A(r) = (pi)(1-r^2)/2

a(r) = 2(pi)(1-r)^2

so A(r)/a(r) = (1+r)/((1-r)*4)

So it looks like the answer would be .5/0 or infinite(undefined)