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'Close to Triangular' printed from https://nrich.maths.org/
Here are the coordinates of nine points. It is possible to draw a
triangle so that the shortest distance from each point to the
triangle is at most one unit.
$(0, 0)$
$(8, 2)$
$(7, 8)$
$(170, 180)$
$(340, 360)$
$(2001, 1000)$
$(1500, 750)$
$(3000, 2000)$
$(4002, 2000)$
Can you find a suitable triangle? Is there more than one
possibility?
Given three points, it is
always possible to draw different
triangles with edges passing through those three points - here are
some examples of triangles going through the same three
points:
Can you convince yourself that there are always
infinitely many such
triangles?
Here are some examples of different triangles going through the
same set of four points:
Is it always possible to draw triangles through a set of four
points, whatever their position?
Investigate some examples and explain your findings.
What happens when we try to draw triangles through five
points?