RU-ALLRUSSIAN 1969 Problem 10
Given a pentagon with equal sides.
(a) Prove that there is a point X on the longest diagonal such that every side subtends an angle at most 90 degrees at X.
(b) Prove that the five circles with diameter one of the pentagon's sides do not cover the pentagon.
Dataset text NuminaMath olympiads. 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.