X256

1st SHARYGIN POINT

X256 = cevapoint of PU(6)
< 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) { 9, 43 }: Central Line L(9, 43) { 8, 192 }: Central Line L(8, 192) { 4, 240 }: Central Line L(4, 240) { 21, 238 }: Central Line L(21, 238) { 1, 511 }: Central Line L(1, 511) { 314, 350 }: Central Line L(314, 350) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_9 = MITTENPUNKT (0.5110, 0.1615) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_8 = NAGEL POINT (0.4694, 0.1333) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_4 = ORTHOCENTER (0.6122, 0.3958) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_1 = INCENTER (0.5714, 0.2333) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) A B C X171 X9 X43 X8 X192 X4 X240 X21 X238 X1 X511 X314 X350 X256 (a, b, c) = (5, 6, 7) | AB = 1

X256 (1st SHARYGIN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{2} + bc) : 1/(b^{2} + ca) : 1/(c^{2} + ab)\)
Barycentrics: \(a/(a^{2} + bc) : b/(b^{2} + ca) : c/(c^{2} + ab)\)
Search Value (6, 9, 13): \(2.007180702620\)
▸ Incident Central Lines15 lines

{1, 511}, {3, 987}, {4, 240}, {7, 982}, {8, 192}, {9, 43}, {21, 238}, {37, 694}, {40, 989}, {55, 983}, {84, 988}, {104, 1064}, {291, 894}, {314, 350}, {573, 981}

▸ Functional Relations8 relations

Notes

See the description at X1281. The lines AD, BE, CF defined there concur in X256.