In my previous post I presented a geometry problem with two equal rectangles in a circle. https://convexabacus.xyz/index.php/2022/04/25/solve-two-equal-rectangles-in-a-circle/
I am happy to report that it was solved by Ed Staples. His solution is shown below, applying the cosine rule on triangle OST, not QTB, which is a typo in the image. Given that the height of the rectangle is 1, he calculates that the width (2a) of the rectangle is sqrt(3)/6 and the radius of the circle is (sqrt(7/3))/2.
There is more than one way to approach this problem. It was solved independently by three members of LinkedIn when Ed posted the problem there. If you don’t know where to start, I suggest looking for 30-60-90 degree triangles in the construction.
I created this construction by exploring several variations using Geogebra and this was the only one I could find that led to a good mathematics problem. A simpler way of fitting two equal rectangles in a circle is left as an exercise for the reader.
