X3169

X6-CEVA CONJUGATE OF X9

< 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, 9 }: Central Line L(8, 9) { 100, 604 }: Central Line L(100, 604) { 6, 979 }: Central Line L(6, 979) { 519, 573 }: Central Line L(519, 573) { 42, 1449 }: Central Line L(42, 1449) { 145, 1400 }: Central Line L(145, 1400) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_9 = MITTENPUNKT (0.5110, 0.1615) X_8 = NAGEL POINT (0.4694, 0.1333) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_979 = -CROSS CONJUGATE OF X(1) (-0.0435, -0.0124) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1449 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(9) (0.5830, 0.2470) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1400 = -BETH CONJUGATE OF X(37) (0.6246, 0.3268) X_3169 = -CEVA CONJUGATE OF X(9) (0.7865, 0.3483) A B C X6 X9 X8 X100 X604 X979 X519 X573 X42 X1449 X145 X1400 X3169 (a, b, c) = (5, 6, 7) | AB = 1

X3169 (X6-CEVA CONJUGATE OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X6 and \(u : v : w\) = X9
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-9.351682741478\)
▸ Incident Central Lines10 lines

{1, 2092}, {6, 979}, {8, 9}, {42, 1449}, {43, 2300}, {100, 604}, {145, 1400}, {284, 2319}, {519, 573}, {1018, 1743}

▸ Functional Relations1 relation