Problem
of the
Week

PROBLEM 247

Start with a circle, C, of radius 1/2 and center b, inside of which you have drawn two circles, L and R, of radius 1/4, so all three circles are mutually tangent. See the figure on the left.  Let a be the center of L and b the point of intersection of L and R.  Draw a circle, T, with center t which is mutually tangent to L, R and C, and a circle with center s which is mutually tangent to T, L, and C.  What is the area of the quadrilateral abst?

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ã2006 Alberto L. Delgado