The triangle is filled with points and labels???

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 $100m+n$ .