# The Most and the Least of Mickey

Geometry Level 5

Two lines intersect each other forming an angle $$a$$. A circle of radius $$r$$ is tangent to both of these lines. Two equal size circles with radius $$R$$ are:

(1): tangent to this circle,
(2): tangent to each other, and
(3): each tangent to one of the lines,

As the size of the angle $$a$$ changes, so does the value of the ratio $$\dfrac Rr$$. If $$m$$ and $$M$$ are the infimum and the supremum of the ratio $$\dfrac Rr$$ respectively, report $$m+M$$.

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