Two circles are inscribed in a rectangle as shown. One diagonal passes through the point of tangency where the two circles touch, and the other diagonal is tangent to the smaller circle.
You may define the radius of the large circle as 1 and the radius of the small circle as r. Can you find an equation for r, and numeric values for r and for the lengths of the sides of the rectangle?
I created this construction using Geogebra, iteratively adjusting it until everything fitted. The aspect ratio of the rectangle turns out to be about 1.72, a fact that can be used to check your own result. The dimensions of the rectangle are not an initial condition, but a consequence of the radii of the two circles. However, as an alternative exercise try drawing this construction yourself, beginning with a 100 by 172 rectangle.
I am delighted to report that this problem was solved independently by Ted Courant and by Keith Raskin after I posted it on the Math, Math Education, Math Culture group on LinkedIn. They also observed that the rectangle is more accurately drawn with side lengths 1003 and 1725.
Great Job!