CEMC Euclid, 2008

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, the large circle has radius $9$ and centre $C(15, 0)$ . The small circles have radius $4$ and centres $A$ and $B$ on the horizontal line $y = 12$ . Each of the two small circles is tangent to the large circle. It takes a bug $5$ seconds to walk at a constant speed from $A$ to $B$ along the line $y = 12$ . How far does the bug walk in $1$ second?

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