Have I drawn this diagram correctly? Cant Solve it, thanks

Question

A, B and C are three points on the circumference of a circle. The tangent to the circle at A makes an angle (Alpha) with the chord AB. The diameter through A cuts the circle again at D and D is joined to B. Prove that Angle ACB = (Alpha).

I have drawn a diagram (link below) but I can't see how the angle at C would be the same as Alpha. Perhaps I haven't drawn the diagram correctly?

 

http://picpaste.com/pics/untitled-haIqm7mz.1445761206.bmp

 

EDIT: I have noticed that if you assume that the question has been written incorrectly and that when D is mentioned, they are really referring to C, then Angle C does solve to equal Alpha. Perhaps it is the question that has been written incorrectly in that case.

Answer 1

The diagram is okay and the problem is valid. An angle XYZ inscribed in a given circular arc is the one where X and Z are endpoints of the arc and Y is anywhere else on the arc. If the arc has angular measure θ then all angles inscribed in it measure θ/2. This is called the Inscribed Angle Theorem (IAT)

 

Proof of the problem using IAT:

Step 1: Since AD is a chord, arc ABD is 180° so by IAT, ∠ABD = 90°.

 

Step2: The diameter AD is perpendicular to the tangent at A so ∠DAB = 90° - α.

 

Step 3: The sum of a triangle's interior angles is 180°. This gives ∠ADB = α.

 

Step 4: ∠ADB and ∠ACB are inscribed in the same arc, so by IAT, ∠ADB =∠ACB. Therefore ∠ACB = α.

Answer 2