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The altitudes through the vertices A,B,C of an acute-angled triangle ABC meet the opposite sides at D,E, F, respectively. The line through D parallel to EF meets the lines AC and AB at Q and R, respectively. The line EF meets BC at P. Prove that the circumcircle of the triangle PQR passes through the midpoint of BC.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1967IMO Shortlist 1997 problem 111
1969IMO Shortlist 1997 problem 132
1972IMO Shortlist 1997 problem 160
1975IMO Shortlist 1997 problem 192
1976IMO Shortlist 1997 problem 200
1982IMO Shortlist 1997 problem 260