In the figure below, E is the midpoint of the arc ABEC and the segment ED is perpendicular to the chord BC at D. If the length of the chord AB is l1, and that of the segment BD is l2, determine the length of DC in terms of l1,l2.
[asy]
unitsize(1 cm);
pair A=2dir(240),B=2dir(190),C=2dir(30),E=2dir(135),D=foot(E,B,C);
draw(circle((0,0),2)); draw(A--B--C); draw(E--D); draw(rightanglemark(C,D,E,8));
label("A",A,.5A); label("B",B,.5B); label("C",C,.5C); label("E",E,.5E); label("D",D,dir(-60));
[/asy] geometryangle bisectorgeometry proposed