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