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'Napoleon's Hat' printed from https://nrich.maths.org/
Why do this problem?
Learners can investigate using the interactivity, make a conjecture
and then try to prove their own conjecture.
It can be an exercise in coordinates.
It is useful for learners to appreciate that the symmetry of the
result makes it unecessaryto work out all three distances.
Possible approach
Ideally learners would work independently on this problem.
Key question
How do we find the coordinates of the centroid of an equilateral
triangle?
Possible
support
GeoGebra is FREE
educational mathematics software and your learners can experiment
with it and draw their own dynamic diagrams.