Question 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.
(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.