Let a⩽b⩽c be non-negative integers. A triangle on a checkered plane with vertices in the nodes of the grid is called an (a,b,c)-triangle if there are exactly a nodes on one side of it (not counting vertices), exactly b nodes on the second side, and exactly c nodes on the third side.[*]Does there exist a (9,10,11)-triangle?
[*]Find all triples of non-negative integers a⩽b⩽c for which there exists an (a,b,c)-triangle.
[*]For each such triple, find the minimum possible area of the (a,b,c)-triangle.Proposed by P. Kozhevnikov geometrylattice pointsKvant