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Longest side of primitive integer triangles with nonzero rational distances between three vertices and first isogonic center, sorted.
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%I #17 May 02 2020 05:28:10

%S 73,95,152,205,208,280,285,287,296,343,361,387,407,437,469,473,485,

%T 497,507,608,624,633,645,713,715,728,728,817,873,931

%N Longest side of primitive integer triangles with nonzero rational distances between three vertices and first isogonic center, sorted.

%H Leisure Maths Entertainment Forum, <a href="http://kuing.orzweb.net/viewthread.php?tid=6994">The primitive integer triangles with nonzero rational distances between three vertices and 1st isogonic center</a>, Chinese blog.

%H Project Euler, <a href="https://projecteuler.net/problem=143">Problem 143. Investigating the Torricelli point of a triangle</a>

%e Case 1: When the isogonic center is inside the triangle, i.e., the three internal angles are all less than 120 degrees: Example: Length of three sides (a, b, c) = (57, 65, 73), rational distances with signs (x, y, z) = (325/7, 264/7, 195/7);

%e Case 2: When the isogonic center is outside the triangle, i.e., an internal angle is greater than 120 degrees. Example: Lengths of three sides (a, b, c) = (43, 248, 285), rational distances with signs (x, y, z) = (1800/7, 345/7, -136/7);

%e Thus 73 and 285 are in this sequence.

%Y Cf. A070082.

%K nonn,more

%O 1,1

%A _Mo Li_, Mar 18 2020