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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