A round table is pushed into a corner — find its diameter from one ink spot
A circular table is pushed into a right-angled corner of a room so its edge touches both walls. Somewhere on the table's rim there's a spot of ink exactly 8 inches from one wall and 9 inches from the other. Without any other measurement, work out the table's full diameter.
Reveal the answer
58 inches. Placing the corner at the origin with the walls along the two axes, the table's centre sits at (r, r) for radius r, and the ink spot at (8, 9) must satisfy (8-r)² + (9-r)² = r². Solving gives r = 29 or r = 5, and only the larger fits a real table pushed into a corner. This is Puzzle No. 97 from Henry Dudeney's 1917 Amusements in Mathematics.
— Henry Ernest Dudeney, Amusements in Mathematics — Puzzle No. 97, 1917