An interesting problem related to Pedal Triangle

Geometry Level 5

Let there be a triangle \(ABC\) with the area of 10 and the radius of its circumcircle of 5. A point \(M\) lies inside the circumcircle of \(ABC\). Suppose a triangle whose side lengths are \(AM.BC, BM.AC, CM.AB \) be called \(\Delta(M) \). Determine the maximum value of the area of \(\Delta(M) \).

Note: A pedal triangle is obtained by projecting a point onto the sides of a triangle.

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