Because triangle ABC is isosceles, and BAC and angle ACB are the same. Draw a line between C and D. Because both BAC and BDC are angles on the same chord, they too are the same.

Triangles BEC and BCD share angle CBD and have another angle in common and are therefore similar.

BC/BE = BD/BC

BD = (BC^2)/BE = 100/4 = 25

Therefore DE = 21.

Interestingly there isn’t enough information to determine the diameter of the circle, but whatever you choose it to be, DE will be equal to 21.