3

Part of 1988 Bundeswettbewerb Mathematik

Problems(2)

octagon [with equal angles and rational sides]

Source:

Consider an octagon with equal angles and with rational sides. Prove that it has a center of symmetry.

geometryparallelogramtrigonometryalgebrapolynomialgeometry solved

orthic triangles of same perimeter criterion on acute triangles

Source: 1988 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p3

Prove that all acute-angled triangles with the equal altitudes

h_c

and the equal angles

\gamma

have orthic triangles with same perimeters.

geometryperimeterorthic triangle