MathDB

regular pyramid and 2n-gon as a base

Source: Problem 5, Polish NO 1992

October 1, 2005

geometry3D geometrypyramidspherevectorgeometry unsolved

Problem Statement

The base of a regular pyramid is a regular

2n

-gon

A_1A_2...A_{2n}

. A sphere passing through the top vertex

S

of the pyramid cuts the edge

SA_i

B_i

(for

i = 1, 2, ... , 2n

). Show that

\sum\limits_{i=1}^n SB_{2i-1} = \sum\limits_{i=1}^n SB_{2i}