Two unit squares are jammed inside a semicircle. The left square, whose base lies on the diameter, has a single vertex touching the circle. The right square, tilted 45 degrees such that one diagonal is perpendicular with the diameter has a vertex touching the diameter, a vertex touching the left square and two vertices touching the circle. Can you find an exact expression for the radius of the circle ?
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[…] As usual, my online colleague Ed Staples has provided a succinct solution to this problem. I attach his diagram and result below. You can see that he began by bisecting the chord AB and drawing the perpendicular bisector MC. He calculated the radius of the circle as an exact expression involving square roots, which has an approximate numeric value of 1.5213. This is in agreement with the value I found experimentally when using Geogebra to create the problem. The problem statement is here: https://convexabacus.xyz/index.php/2022/04/11/two-unit-squares-in-a-semicircle/ […]