# Geometricus geometriorum (HP II, secret "semi-tyre")

Geometry Level 5

A semicircumference of radius $$\pi$$ is divided into $$n + 1$$ equal parts and is joined any point of the division with the ends of the semicircumference, forming a right-triangle with area $$A_{k}$$ .

Find the limit as n tends to infinity of the arithmetic mean of the areas of these triangles.

inspiration

Bonus: Generalise when the radius is $$r$$

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