X1199

3rd SARAGOSSA POINT OF X54

X1199 = crosspoint of X54 and X1173
< 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) { 4, 6 }: Van Aubel Line { 23, 143 }: Central Line L(23, 143) { 54, 186 }: Central Line L(54, 186) { 140, 195 }: Central Line L(140, 195) { 288, 1157 }: Central Line L(288, 1157) { 578, 1204 }: Central Line L(578, 1204) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_1173 = 1st SARAGOSSA POINT OF X(54) (0.6043, 0.2952) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_143 = NINE-POINT CENTER OF ORTHIC TRIANGLE (0.6358, 0.3534) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_288 = CEVAPOINT OF X(6) AND X(54) (0.5936, 0.2442) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_578 = ORTHOHARMONIC OF X(216) (0.5933, 0.2561) X_1204 = 3rd SARAGOSSA POINT OF X(64) (0.6497, 0.1923) X_1199 = 3rd SARAGOSSA POINT OF X(54) (0.5984, 0.2504) A B C X54 X1173 X4 X6 X23 X143 X186 X140 X195 X288 X1157 X578 X1204 X1199 (a, b, c) = (5, 6, 7) | AB = 1

X1199 (3rd SARAGOSSA POINT OF X54) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1166)
Search Value (6, 9, 13): \(2.580907288249\)
▸ Incident Central Lines7 lines

{4, 6}, {5, 3410}, {23, 143}, {54, 186}, {140, 195}, {288, 1157}, {578, 1204}

▸ Functional Relations3 relations