# 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 $$100m+n$$.

×