IMO Shortlist 1960 problem 7

  Avg: 0,0
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
An isosceles trapezoid with bases a and c and altitude h is given.

a) On the axis of symmetry of this trapezoid, find all points P such that both legs of the trapezoid subtend right angles at P;

b) Calculate the distance of p from either base;

c) Determine under what conditions such points P actually exist. Discuss various cases that might arise.
Izvor: Međunarodna matematička olimpijada, shortlist 1960