MathDB

124

Part of 1969 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 124 All Soviet Union MO 1969 pentagon with equal sides

Source:

6/23/2019
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 ABAB is seen from the point CC inside an arbitrary angle that is greater or equal than ∠ACB\angle ACB)
b) Prove that the circles constructed on its sides as on the diameters cannot cover the pentagon entirely.
geometrypentagon