8. Let ABC be a triangle and denote by A1, A2 the points on the rays opposite to
AB, AC, respectively, satisfying AA1 = AA2 = BC (i.e. A1 is on line AB with A
between A1 and B). Define points B1, B2, C1, C2 analogously. Prove that points
A1, A2, B1, B2, C1, C2 lie on a single circle.
