Pythagorean Theorem Proof Without Words 6 Your punishment for awarding me a "Nice Question" badge for my last question is that I'm going to post another one from Proofs without Words.
How does the attached figure prove the Pythagorean theorem?

P.S. No, I will not go through the entire book page-by-page asking for help.
P.P.S. No, I am not a shill for the book. Just a curious math student.

I think the picture is missing two more lines: those connecting all the points on the circle. Once these segments are drawn, we see two important right-angled triangles: one has sides $c+a$, $b$ and the hypotenuse; the other has sides $c-a$ and $b$ and the hypotenuse. A quick counting of angles shows that these two triangles are similar, hence we obtain the ratio written on the left:
$$
\frac{c+a}{b} = \frac{b}{c-a}.
$$
And the theorem follows from this ratio by 'cross multiplying'.
