# Which center are we referring to again?

Geometry Level 5

Given the triangle $$ABC$$ with vertices on a circle such that $$\overline { AB } =11,\quad \overline { BC } =13,\quad \overline { CA } =16$$

Let $$I$$ be the incenter and $$O$$ the circumcenter.

If the value of $$\overline { IO }^2$$ is of the form $$\frac { x }{ y }$$ for coprime positive integers, what is the value of $$x+y$$?

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