MathDB

Let

k

be a circle and

k_{1},k_{2},k_{3},k_{4}

four smaller circles with their centres

O_{1},O_{2},O_{3},O_{4}

respectively, on

k

. For i \equal{} 1,2,3,4 and k_{5}\equal{} k_{1} the circles

k_{i}

and k_{i\plus{}1} meet at

A_{i}

and

B_{i}

such that

A_{i}

lies on

k

. The points

O_{1},A_{1},O_{2},A_{2},O_{3},A_{3},O_{4},A_{4}

lie in that order on

k

and are pairwise different. Prove that

B_{1}B_{2}B_{3}B_{4}

is a rectangle.

Problem Statement