Browse · MathNet
Print60th Belarusian Mathematical Olympiad
Belarus geometry
Problem
Is it possible to mark 8 distinct points (1 red, 3 blue, and 4 green points) on a plane so that the sum of the distances between the red point and the blue points is 6, the sum of the distances between the red point and the green points is 16, and the sum of the distances between the blue points and the green points is 56?
Solution
For example, the points can be marked on the straight line in the following way: the blue points have the coordinates , , , the red point has the coordinate , and the green points have the coordinates , , , .
Final answer
Yes; for example, place the blue points at -3, -1, 2; the red point at 0; and the green points at 3, 3.5, 4.5, 5.
Techniques
Cartesian coordinatesDistance chasing