%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