Pythagorean Theorem Proof Without Words 6

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 $c^2-a^2=b^2$.

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'.

I will try to complete the answer of @Rick. The two triangles ABD and ADE are the same because both have the same angles 90, alpha and 90-alpha.

And we have $Cotangent(alpha) = \frac{BD}{DA} = \frac{AD}{DE} = \frac{c+a}{b} = \frac{b}{c-a}$