Solidify your plane geometry for RMO: Archimedes Problem

Solve the following historically famous problem (Archimedes):

On a circular arc AB, the point M is midway, that is, arc AM is equal to arc MB. The point C is on the arc MB. The point D is the foot of the perpendicular from M onto the line AC. Prove that D is the mid-point of the straight line path AC + CB.

Nalin Pithwa.

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