The answer to this is 2.
There are a number of proofs to this. Here, we use Euclidean geometry with trigonometry. If we let the center of the circle to be O.
Then, we have the following equations for the angles
CEO = OED = 90
Since, CO = OD because they're radii of the circle, then
ΔCOD is an isosceles triangle and
OCE = ODE
CE + DE = CD
dividing the whole equation by DE
CE/DE + 1 = CD/DE
Using trigonometric functions:
CE = OC cos OCE and
DE = OD cos ODE
Substituting.
OC cos OCE / OD cos ODE + 1 = CD/DE
Since, OCE = ODE,
cos OCE = cos ODE
The equation would be reduced to:
1 + 1 = CD/DE
CD/DE =2
