Expand BA and CD to g.
∫AD/BC = 1/3
∴S△GAD/S△GBC= 1/9
Sadef = sefbc again
∴S△GEF/S△GBC=5/9
∴GE/GB=√5/3
And GA/GB=AD/BC= 1/3.
∴AE/GB=(√5- 1)/3
∴BE/GB=(3-√5)/3
∴BE/AB=(3-√5)/2
And CF/CD=BE/AB.
∴BE+CE= 15-5√5