X1469

X984-BETH CONJUGATE OF X984

X1469 = X1350-of-Mandart-incircle-triangle
< 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) { 7, 8 }: Gergonne–Nagel Line { 6, 41 }: Central Line L(6, 41) { 43, 57 }: Central Line L(43, 57) { 12, 141 }: Central Line L(12, 141) { 36, 182 }: Central Line L(36, 182) { 1, 256 }: Central Line L(1, 256) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_1 = INCENTER (0.5714, 0.2333) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_1469 = -BETH CONJUGATE OF X(984) (0.6171, 0.3088) A B C X984 X7 X8 X6 X41 X43 X57 X12 X141 X36 X182 X1 X256 X1469 (a, b, c) = (5, 6, 7) | AB = 1

X1469 (X984-BETH CONJUGATE OF X984) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a (b^{2} + b c + c^{2})/(a - b - c) : :\)
Search Value (6, 9, 13): \(0.370774743273\)
▸ Incident Central Lines16 lines

{1, 256}, {3, 611}, {6, 41}, {7, 8}, {12, 141}, {36, 182}, {42, 1403}, {43, 57}, {51, 614}, {55, 1350}, {109, 753}, {193, 330}, {222, 1460}, {613, 999}, {751, 1319}, {970, 888}

▸ Functional Relations3 relations