MathDB

3

Part of 1988 Polish MO Finals

Problems(2)

Polygon with a center of symmetry

Source: Problem 3, Polish NO 1988

10/16/2005
WW is a polygon which has a center of symmetry SS such that if PP belongs to WW, then so does P′P', where SS is the midpoint of PP′PP'. Show that there is a parallelogram VV containing WW such that the midpoint of each side of VV lies on the border of WW.
symmetrygeometryparallelogramgeometry unsolved
Tetrahedron inside a hemisphere of radius 1

Source: Problem 6, Polish NO 1988

10/16/2005
Find the largest possible volume for a tetrahedron which lies inside a hemisphere of radius 11.
geometry3D geometrytetrahedronspheretrigonometrygeometry unsolved