Tessellate S.T.E.M.S - Mathematics - School - Set 2 - Problem 3

There are $13$ points marked on a square of side length $1$ , no three of which lie in a straight line.

$\textbf{Statement 1}$ . There exist $2$ points among the given points with distance less than or equal to $\frac{5}{12}$ .

$\textbf{Statement 2}$ . Among the given points, there exist $4$ points which lie on a circle.

Which of the above statements are correct?

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This problem is a part of Tessellate S.T.E.M.S.