4th All Soviet Union Mathematical Olympiad 1970 Problems & Solutions

1.  Given a circle, diameter AB and a point C on AB, show how to construct two points X and Y on the circle such that (1) Y is the reflection of X in the line AB, (2) YC is perpendicular to XA. 2.  The product of three positive numbers is 1, their sum is greater than the sum of their inverses. Prove that just one of the numbers is greater than 1. 3.  What