Problem

Source: China TST 2004 Quiz

Tags: geometry, perimeter, inequalities, trigonometry, trig identities, Law of Sines, geometry unsolved



Convex quadrilateral ABCD is inscribed in a circle, A=60o, BC=CD=1, rays AB and DC intersect at point E, rays BC and AD intersect each other at point F. It is given that the perimeters of triangle BCE and triangle CDF are both integers. Find the perimeter of quadrilateral ABCD.