X1476

X1222-BETH CONJUGATE OF X1222

X1476 = cevapoint of X1 and X56
< 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, 56 }: Central Line L(8, 56) { 172, 294 }: Central Line L(172, 294) { 4, 496 }: Central Line L(4, 496) { 9, 604 }: Central Line L(9, 604) { 3, 1000 }: Central Line L(3, 1000) { 1, 1106 }: Central Line L(1, 1106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1222 = ISOGONAL CONJUGATE OF X(1201) (0.5108, 0.1870) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_4 = ORTHOCENTER (0.6122, 0.3958) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_9 = MITTENPUNKT (0.5110, 0.1615) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1000 = ISOGONAL CONJUGATE OF X(999) (0.5463, 0.1961) X_1 = INCENTER (0.5714, 0.2333) X_1106 = TRILINEAR SQUARE OF X(56) (0.6507, 0.4375) X_1476 = -BETH CONJUGATE OF X(1222) (0.5968, 0.2987) A B C X1222 X8 X56 X172 X294 X4 X496 X9 X604 X3 X1000 X1 X1106 X1476 (a, b, c) = (5, 6, 7) | AB = 1

X1476 (X1222-BETH CONJUGATE OF X1222) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{2} (\sin^{2}(B/2) + \sin^{2}(C/2))) : :\)
Search Value (6, 9, 13): \(0.519305962588\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(1/[(\sin B) \tan(B/2) + (\sin C) \tan(C/2)] : :\)

  • Trilinears: \(1/[(b + c - a)(b^{2} + c^{2} - 2bc + ab + ac)] : :\)

▸ Incident Central Lines14 lines

{1, 1106}, {3, 1000}, {4, 496}, {8, 56}, {9, 604}, {21, 1319}, {65, 1320}, {80, 1210}, {172, 294}, {256, 1458}, {314, 1014}, {651, 1201}, {942, 1389}, {943, 1385}

▸ Functional Relations4 relations