AB and AD are tangents of the circle with the center at C. The measure of BDC = 45o, and the circle has a diameter of 4. Which is the length of AB?

Answer 1

Tricky little question.
On my second attempt at the diagram I realized that in triangle BDC , the central angle had to be 90°
So the diagram really just consists of a square with sides 2.
So without any further calculations because of the properties of a square

AB = 2

The key lies in a proper diagram.