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## 'Close to Triangular' printed from http://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?