Well?
71.86%
full circle
probably has something to do with the Pythagorean theorem
The key condition is that there is a diameter going through the center of the tile and it should meet an edge of the tile at its very end. Let's say the domino is 1x2 and the circle has radius x. The small right-angled triangle whose hypothenuse goes from the center of the tile to the center of the circle has with legs 1-x and x-1/2 and is similar to the larger one whose hypothenuse goes from the center of the circle to the point where the diameter meets the edge of the tile, which has a small leg of 1-x and a hypothenuse of x. Therefore (x-1/2)/(1-x)=(1-x)/√[x2-(1-x)2].Numerical solver says x ≈ 0.67636, which gives a solution of 0.676362π/2 ≈ 71.858%. A quick construction using CAD gives the same number. If you want the exact solution, WolframAlpha says x should be picrel.Who exactly should be able to solve this by hand?
