Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Let $AB$ be a diameter of a circle centered at $O$.  Let $E$ be a point on the circle, and let the tangent at $B$ intersect the tangent at $E$ and $AE$ at $C$ and $D$, respectively.  If $\angle BAE = 43^\circ$, find $\angle CED$, in degrees.

[asy]
import graph;

unitsize(2 cm);

pair O, A, B, C, D, E;

O = (0,0);
A = (0,1);
B = (0,-1);
E = dir(-6);
D = extension(A,E,B,B + rotate(90)*(B));
C = extension(E,E + rotate(90)*(E),B,B + rotate(90)*(B));

draw(Circle(O,1));
draw(B--A--D--cycle);
draw(B--E--C);

label("$A$", A, N);
label("$B$", B, S);
label("$C$", C, S);
label("$D$", D, SE);
label("$E$", E, dir(0));
dot("$O$", O, W);
[/asy]
user