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In this talk I have a simple aim: to present a conjecture regarding the rule the ancient Egyptian geometers employed to compute the area of a circle and to attribute a value to $\pi$. To this end, I shall consider the two particular problems, the problems 48 and 50, which are generally uttered as the main sources of information about this Egyptian rule. These two problems are stated in the Rhind Mathematical Papyrus (RMP), which is one of the surviving and major sources to illustrate the level and scope of the mathematical knowledge of the ancient Egyptians.