Proving two bisectors are equal

In a triangle ABC, angle B is 60 degrees. Angles A and C are bisected to points D and E respectively, on the edge of the triangle (see diagram). They cross at point O. Prove that OD = OE

http://i301.photobucket.com/albums/n.../Noether13.jpg

I've gone through it a little and got this.

2x + 2y + 60 = 180

2x + 2y = 120

x + y = 60

I don't know if this helps at all.

Remember, angles A and C are bisected, so the two adjacent angles are equal to each other (x, x and y, y)

Thanks for any help, BG