math

posted by halp

In the below figure, EB is tangent to the circle with center $C$ at the point B. If EC is equal to the diameter of the circle, find the measure of angle BAD in degrees.

and here is the ugly LaTeX
[asy]
pair C = (0,0), B = dir(110), D = dir(170), E2 = 2 * D, A = dir (305);
draw(unitcircle);
draw(C--E2--B--C^^D--A--B);
dot(A^^B^^C^^D^^E2);
label("$A$",A,SE);
label("$B$",B,NW);
label("$C$",C,S);
label("$D$",D,SW);
label("$E$",E2,W);
[/asy]

1. Reiny

I can draw the circle, its centre O, and the tangent EB.
Where is A and D in angle BAD ???
I can find the central angle BCE by
cos BCE = r/(2r) = 1/2
so angle BCE = 60° , which makes angle BEC = 30°

Does that help?

2. Charlie

thanks that helped a lot

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