At least there's a diagram

Geometry Level 3

In triangle $$ABC$$ we have $$AB=36$$, $$BC=48$$, $$CA=60$$. The incircle of $$ABC$$ is centered at $$I$$ and touches $$AB$$, $$AC$$, $$BC$$ at $$M$$, $$N$$, $$D$$, respectively. Ray $$AI$$ meets $$BC$$ at $$K$$. The radical axis of the circumcircles of triangles $$MAN$$ and $$KID$$ intersects lines $$AB$$ and $$AC$$ at $$L_1$$ and $$L_2$$, respectively. If $$L_1L_2 = x$$, compute $$x^2$$.

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