IMO Shortlist 1995 problem G4
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Avg: 7,0 An acute triangle is given. Points and are taken on the side (with between and ), and on the side (with between and ), and and on the side (with between and ) so that
The lines and bound a triangle, and the lines and bound a second triangle. Prove that all six vertices of these two triangles lie on a single circle.
The lines and bound a triangle, and the lines and bound a second triangle. Prove that all six vertices of these two triangles lie on a single circle.
Izvor: Međunarodna matematička olimpijada, shortlist 1995