From the question "Sangaku Circle Geometry Problem":
Given $a$ and $b$, find $c$. (The enclosing circular segment is not necessarily a semicircle.)
The answer is
$$c = \frac{a(\sqrt{a} + \sqrt{b})^2}{4(3b + \sqrt{ab} )}$$
I'm curious how one would solve the given puzzle using a system of equations.
My first attempt was to describe all circles via the circle formula: $$(x−m_1)^2+(y−m_2)^2=r^2$$ with $$r=a,b,c,d$$ accordingly for every circle and equate the circle equations of touching circles in certain points. But I didn't got the clue how I should state the midpoints of the circles.
Maybe someone could give me a little push in the right direction.