arithmetic mean of areas of triangles by n+1 points on semicircle and 2 ends
Source: Spanish Mathematical Olympiad 1983 P3
December 23, 2022
geometrycombinatorial geometrycombinatoricsarea of a triangle
Problem Statement
A semicircle of radius is divided into equal parts and any point of the division with the ends of the semicircle forms a triangle . Calculate the limit, as tends to infinity, of the arithmetic mean of the areas of the triangles.