convex pentagon drawn by diagonals of regular pentagon
Source: Spanish Mathematical Olympiad 1966 P3
December 4, 2022
geometrysimilaritypentagon
Problem Statement
Given a regular pentagon, consider the convex pentagon limited by its diagonals. You are asked to calculate:
a) The similarity relation between the two convex pentagons.
b) The relationship of their areas.
c) The ratio of the homothety that transforms the first into the second.