# Construct a Circle

Geometry Level 4

It is well known that three noncollinear points in a plane uniquely determine a circle. Let $$(u,v)$$ be the center of the circle containing the three points $$A = (1,2)$$, $$B = (5,8)$$, and $$C = (10,7)$$. Then $$u+v$$ can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. Find $$a+b$$.

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