« Vrati se
Let k be a circle and k_{1},k_{2},k_{3},k_{4} four smaller circles with their centres O_{1},O_{2},O_{3},O_{4} respectively, on k. For i = 1,2,3,4 and k_5=k_1 the circles k_i and k_{i+1} meet at A_i and B_i such that A_i lies on k. The points O_{1},A_{1},O_{2},A_{2},O_{3},A_{3},O_{4},A_{4} lie in that order on k and are pairwise different.

Prove that B_{1}B_{2}B_{3}B_{4} is a rectangle.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1568IMO Shortlist 1981 problem 110
1502IMO Shortlist 1977 problem 40
1483IMO Shortlist 1975 problem 120
1447IMO Shortlist 1973 problem 50
1444IMO Shortlist 1973 problem 20
1417IMO Shortlist 1971 problem 40