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 diagram ought to include lines that connect all the three points on the large circle into a triangle. It is then (I think) supposed to be known that an inscribed triangle that has a diameter as one of its sides is right, and that an altitude towards the hypotenuse divides a right triangle into two similar triangle. The proportion $\frac{c+a}{b}=\frac{b}{c-a}$ then comes from these two similar triangles. Cross multiplying with the denominators produces $c^2-a^2=b^2$.
