# Equilateral Triangle with X Inside

Geometry Level 5

$$ABC$$ is an equilateral triangle with side length $$N$$. $$X$$ is a point within $$ABC$$, such that the distance from $$X$$ to the vertices $$A, B, C$$ are $$8$$, $$13$$ and $$15$$, respectively. What is the value of $$N^2$$?

×