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0262 geometry 2nd edition Round 6 p2
Source:
5/10/2021
A triangle
A
B
C
ABC
A
BC
is located in a cartesian plane
π
\pi
π
and has a perimeter of
3
+
2
3
3 + 2\sqrt3
3
+
2
3
. It is known that the triangle
A
B
C
ABC
A
BC
has the property that any triangle in the plane
π
\pi
π
, congruent with it, contains inside or on the boundary at least one lattice point (a point with both coordinates integers). Prove that the triangle
A
B
C
ABC
A
BC
is equilateral.
geometry
2nd edition