5th International Mathematical Olympiad 1963 Problems & Solutions

A1.  For which real values of p does the equation         √(x2 - p) + 2 √(x2 - 1) = x have real roots? What are the roots? A2.  Given a point A and a segment BC, determine the locus of all points P in space for which ∠APX = 90o for some X on the segment BC. A3.  An n-gon has all angles equal and the lengths of consecutive sides satisfy a1 ≥ a2 ≥ ... ≥ an. Prove