VMO 1989 Problem 3
ABCD is a square side 2. The segment AB is moved continuously until it coincides with CD (note that A is brought into coincidence with the opposite corner). Show that this can be done in such a way that the region passed over by AB during the motion has area < 5π/6.
Community text Kalva (prase.cz mirror). Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.