Task 525

The task

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]