Let A, B, C, D lie on a circle such that A, B, C, D are not form an Isosceles trapezoid. Let AB meets CD at E and AD meets BC at F. Define l(n, m, T) is a line through triangle center X(n), X(m) of triangle T, then l(n, m, ABF), l(n, m, CDF), l(n, m, ADE), l(n, m, BCE) form a cyclic quadrilateral for every positive integer n, m (n \neq m).
Whre X(n) refer to Kimberling triangle center.
