# Pointed Pointy Triangle (My bad sense of naming things)

**Calculus**Level 5

If the average distance from a point randomly selected in the unit equilateral triangle to its center equals
\[\frac{\ln(a+\sqrt{b})+a\sqrt{b}}{c}\]
where \(a,b\) and \(c\) are positive integers with \(b\) being square-free. Find \(a+b+c\).