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IMSO 2018 — Math Division — Exploration Question 3

IMSO Maths · IMSO 2018 — Math Division — Exploration

Question 3

There are 5 points on the plane, such that no three points lie on one line. Every pair of points is connected by a segment. It is known that it is possible to colour five of these segments in red and the rest in blue, so that all segments of each colour form a simple pentagon. Draw one example.

The diagrams below are some examples of a simple pentagon:

Question illustration

The following diagrams below are NOT simple pentagons (because of self intersections):

Question illustration