PL-OM 1992 Problem 5

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 $SA_i$ at $B_i$ (for $i = 1, 2, ... , 2n$ ). Show that $\sum\limits_{i=1}^n SB_{2i-1} = \sum\limits_{i=1}^n SB_{2i}$ .