MathDB

Three circles in the plane, whose interiors have no common point, meet each other at three pairs of points:

A_1

and

A_2

B_1

and

B_2

, and

C_1

and

C_2

, where points

A_2,B_2,C_2

lie inside the triangle

A_1B_1C_1

. Prove that

A_1B_2 \cdot B_1C_2 \cdot C_1A_2 = A_1C_2 \cdot C_1B_2 \cdot B_1A_2 .

Problem Statement