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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