The triangle is filled with points and labels???

Geometry Level 5

Let \(ABC\) be a triangle with circumcenter \(O\) and let \(X,Y,Z\) be the midpoints of the arcs \(BAC,ABC,ACB\) on its circumcircle. Let \(G\) and \(I\) be the centroid of the triangle \(XYZ\) and the incenter of the triangle \(ABC\). Given \(AB=13, BC=14, CA=15\) and \(\frac{GO}{GI}=\frac{m}{n}\) for relatively prime positive integers \(m\) and \(n\). Compute \(100m+n\).

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