some vertices of regular pyramids form a regular hexagon
Source: Brazilian Mathematical Olympiad 1983 P2
July 27, 2018
geometryEquilateral Triangle3D geometrypyramidhecagon
Problem Statement
An equilateral triangle has side a. A square is constructed on the outside of each side of the triangle. A right regular pyramid with sloping side is placed on each square. These pyramids are rotated about the sides of the triangle so that the apex of each pyramid comes to a common point above the triangle. Show that when this has been done, the other vertices of the bases of the pyramids (apart from the vertices of the triangle) form a regular hexagon.