Translated task text
In this task you are going to work with certain type of proof for the (inscribed angel sentence?). The proof has three steps, as illustrated below. On the figures we have used (all those fancy greek letters). The inscribed angle sentence says $\alpha = \frac{\beta}{2}$. Write an explanation for the proof. Try to convey the idea behind each step, and after that the proof as a whole.
Now for the first circel I have the following.
$180-2\alpha$
$\beta = 180 - (180 -2\alpha)$
$\alpha = \frac{\beta}{2}$
This was fine, the proof here is spesific for when one chord is on the diameter. The scond picture you use what "discovered" in the first picture, and prove it for when S is exterior. On the third you don't use anything from the other steps.
Now I'm not sure what the question is here. I have gone through the individual proofs for each of these steps during other tasks in the book. I'm just a bit unsure about the proof as a whole. Is that just the point that with these three steps every possible layout of this figure has been covered? It's just so abstract. I'm reading on my own and would love any input.