Originally Posted by
Debsta Yes angle EDC = angle DCA (alternate angles)
Also, angle DCA = angle ECD (because CD bisects angle BCA)
This makes triangle DCE an isosceles triangle and so DE = 5.
Now look at triangle DBE:
angle DBE = angle ACB (since triangle ABC is isosceles)
Also angle ACB = angle DEB (corresponding angles)
So angle DEB = angle DBE, making DBE an isosceles triangle and therefore DB = DE = 5.
Now AC = AB = AD+DB = 6+5 = 11. (I don't agree that the answer is 10, unless EC=4 rather than 5.)