X1727

MIMOSA TRANSFORM OF X80

X1727 = X4-aleph conjugate of X1718
< 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, 46 }: Central Line L(4, 46) { 35, 72 }: Central Line L(35, 72) { 30, 80 }: Central Line L(30, 80) { 63, 519 }: Central Line L(63, 519) { 1, 1399 }: Central Line L(1, 1399) { 109, 1725 }: Central Line L(109, 1725) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1 = INCENTER (0.5714, 0.2333) X_1399 = -BETH CONJUGATE OF X(35) (0.6178, 0.2762) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1725 = MIMOSA TRANSFORM OF X(74) (0.9993, 0.7957) X_1727 = MIMOSA TRANSFORM OF X(80) (1.2736, 0.8828) A B C X4 X46 X35 X72 X30 X80 X63 X519 X1 X1399 X109 X1725 X1727 (a, b, c) = (5, 6, 7) | AB = 1

X1727 (MIMOSA TRANSFORM OF X80) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X80
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.658728542164\)
▸ Incident Central Lines8 lines

{1, 1399}, {4, 46}, {30, 80}, {35, 72}, {36, 1768}, {63, 519}, {109, 1725}, {1718, 1735}

▸ Functional Relations1 relation