X87

X2-CROSS CONJUGATE OF X1

X87 = isogonal conjugate of X43
< 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) { 6, 43 }: Central Line L(6, 43) { 1, 192 }: Central Line L(1, 192) { 34, 242 }: Central Line L(34, 242) { 56, 238 }: Central Line L(56, 238) { 9, 292 }: Central Line L(9, 292) { 10, 979 }: Central Line L(10, 979) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_9 = MITTENPUNKT (0.5110, 0.1615) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_979 = -CROSS CONJUGATE OF X(1) (-0.0435, -0.0124) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) A B C X2 X1 X6 X43 X192 X34 X242 X56 X238 X9 X292 X10 X979 X87 (a, b, c) = (5, 6, 7) | AB = 1

X87 (X2-CROSS CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(ab + ac - bc) : 1/(bc + ba - ca) : 1/(ca + cb - ab)\)
Barycentrics: \(a/(ab + ac - bc) : b/(bc + ba - ca) : c/(ca + cb - ab)\)
Search Value (6, 9, 13): \(5.357195925405\)
▸ Incident Central Lines8 lines

{1, 192}, {6, 43}, {9, 292}, {10, 979}, {34, 242}, {56, 238}, {58, 978}, {106, 932}

▸ Functional Relations8 relations