ASU 124 All Soviet Union MO 1969 pentagon with equal sides
Source:
June 23, 2019
geometrypentagon
Problem Statement
Given a pentagon with all equal sides. a) Prove that there exist such a point on the maximal diagonal, that every side is seen from it inside a right angle. (side is seen from the point inside an arbitrary angle that is greater or equal than )b) Prove that the circles constructed on its sides as on the diameters cannot cover the pentagon entirely.