sum of lengths of blue segments equals that of red ones, circle, rhombus
Source: TOT 507 1996 Autumn J O4 Tournament Of Towns
August 16, 2024
geometrycirclerhombus
Problem Statement
A circle cuts each side of a rhombus twice thus dividing each side into three segments. Let us go around the perimeter of the rhombus clockwise beginning at a vertex and paint these segments successively in red, white and blue. Prove that the sum of lengths of the blue segments equals that of the red ones.(V Proizvolov)