X1961

CROSSSUM OF PU(31)

X1961 = cevapoint of X846 and X1051
< 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) { 1, 2 }: Nagel Line { 37, 171 }: Central Line L(37, 171) { 35, 199 }: Central Line L(35, 199) { 81, 756 }: Central Line L(81, 756) { 111, 831 }: Central Line L(111, 831) { 86, 1215 }: Central Line L(86, 1215) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_1051 = POINT ALGORAB (0.5863, 0.2501) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_111 = PARRY POINT (0.9885, -0.0457) X_831 = o-(1, 3) CIRCUMCIRCLE POINT (0.1595, 0.4822) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_1961 = CROSSSUM OF PU(31) (0.5631, 0.2252) A B C X846 X1051 X1 X2 X37 X171 X35 X199 X81 X756 X111 X831 X86 X1215 X1961 (a, b, c) = (5, 6, 7) | AB = 1

X1961 (CROSSSUM OF PU(31)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a + b)(a + c) + (b + c)^{2}\)
Search Value (6, 9, 13): \(1.896400730806\)
▸ Incident Central Lines9 lines

{1, 2}, {35, 199}, {37, 171}, {81, 756}, {86, 1215}, {100, 1255}, {111, 831}, {940, 984}, {1051, 1100}

▸ Functional Relations3 relations