X585

1st CONGRUENT SHRUNK INSQUARES POINT

For a discussion, see Floor van Lamoen, “Vierkanten in een driehoek: 5. Gekrompen ingeschreven vierkanten”
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 8, 192 }: Central Line L(8, 192) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_585 = 1st CONGRUENT SHRUNK INSQUARES POINT (0.5354, 0.1924) A B C X8 X192 X585 (a, b, c) = (5, 6, 7) | AB = 1

X585 (1st CONGRUENT SHRUNK INSQUARES POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [2 \operatorname{area} (1/b + 1/c - 1/a) + b + c - a]/a\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = 2 \operatorname{area} (1/b + 1/c - 1/a) + b + c - a\)
Search Value (6, 9, 13): \(2.996078921948\)
▸ Incident Central Lines1 line

{8, 192}

▸ Functional Relations1 relation