Question 20
Triangle $ABC$ has $AB=13,$ $BC=14,$ and $AC=15.$ The points $D,$ $E,$ and $F$ are the midpoints of $AB,$ $BC,$ and $AC$ respectively. Let $X\ne E$ be the intersection of the circumcircles of $\triangle BDE$ and $\triangle CEF.$ What is $XA+XB+XC?$