MathDB

3

Part of 1987 Vietnam National Olympiad

Problems(2)

n points on a plane

Source: Vietnam NMO 1987 Problem 3

2/4/2009
Let be given n≥2 n \ge 2 lines on a plane, not all concurrent and no two parallel. Prove that there is a point which belongs to exactly two of the given lines.
combinatorics unsolvedcombinatorics
Five rays in space

Source: Vietnam NMO 1987 Problem 6

2/4/2009
Prove that among any five distinct rays Ox Ox, Oy Oy, Oz Oz, Ot Ot, Or Or in space there exist two which form an angle less than or equal to 90∘ 90^{\circ}.
geometry3D geometryspherevectoranalytic geometrypyramidgeometry unsolved