# 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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