Sangakus are votive math problems in Japanese temples.
There are hundreds of remaining Sangakus, see references at wasan
There are many very hard Sangakus, and they often involve tough calculations.
One of the simplest, although interesting, is to inscribe two squares and a circle in a larger circle.
The problem is mainly to find different size
(Two equal squares is quite easier, as the figure is symetric.)
Find a condition relating a and b to R.
Give a simple relation for radius ρ.
Find a construction of the figure.
Conversedly, given the two circles, construct the squares.
Details (with JavaSketchpad applets)