4
Part of 1984 Bundeswettbewerb Mathematik
Problems(2)
total length of the irrigation ditches > 70, in square 12x12
Source: 1984 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4
11/21/2022
In a square field of side length there is a source that contains a system of straight irrigation ditches. This is laid out in such a way that for every point of the field the distance to the next ditch is at most . Here, the source is as a point and are the ditches to be regarded as stretches. It must be verified that the total length of the irrigation ditches is greater than m. The sketch shows an example of a trench system of the type indicated.
https://cdn.artofproblemsolving.com/attachments/6/5/5b51511da468cf14b5823c6acda3c4d2fe8280.png
combinatoricscombinatorial geometrygeometric inequalitygeometry
quadrilateral is space
Source: Bundeswettbewerb Mathematik 1984, second stage, problem 4
5/14/2004
A sphere is touched by all the four sides of a (space) quadrilateral. Prove that all the four touching points are in the same plane.
geometry3D geometryspheregeometry solved