X1918

BICENTRIC SUM OF PU(12)

X1918 = isogonal conjugate of X310
< 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, 31 }: Central Line L(6, 31) { 10, 82 }: Central Line L(10, 82) { 86, 171 }: Central Line L(86, 171) { 32, 560 }: Central Line L(32, 560) { 100, 715 }: Central Line L(100, 715) { 101, 729 }: Central Line L(101, 729) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_560 = 4th POWER POINT (0.6520, 0.3639) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_715 = EVEN (- 3, - 1) CIRCUMCIRCLE POINT (1.0000, 0.2040) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_1918 = BICENTRIC SUM OF PU(12) (0.6333, 0.3163) A B C X310 X6 X31 X10 X82 X86 X171 X32 X560 X100 X715 X101 X729 X1918 (a, b, c) = (5, 6, 7) | AB = 1

X1918 (BICENTRIC SUM OF PU(12)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3}(b + c)\)
Search Value (6, 9, 13): \(0.386710974876\)
▸ Incident Central Lines11 lines

{6, 31}, {9, 981}, {10, 82}, {32, 560}, {86, 171}, {100, 715}, {101, 729}, {213, 872}, {313, 983}, {393, 465}, {692, 1333}

▸ Functional Relations6 relations