4
Part of 2002 Bundeswettbewerb Mathematik
Problems(2)
12-gon with sidelengths 1, 2, ..., 12 (not geometry)
Source: German Math. Competition BWM 2002, 1st round, problem 4
11/19/2005
Consider a -gon with sidelengths , , , , ..., .
Prove that there are three consecutive sides in this -gon, whose lengths have a sum .
geometry
bissectors and altitudes
Source: Second round Germany 2002
9/1/2005
In an acute-angled triangle , we consider the feet and of the altitudes from and , and the intersections and of the angle bisectors from and with the opposite sides and respectively. Show that the centre of the incircle of triangle lies on the segment if and only if the centre of the circumcircle of triangle lies on the segment .
geometrycircumcirclesearchincenteranalytic geometryratiotrigonometry