X45

X9-BETH CONJUGATE OF X1

X45 is the {X1,X9}-harmonic conjugate of X44.
< 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) { 1, 6 }: Incenter–Symmedian Line { 2, 88 }: Central Line L(2, 88) { 53, 281 }: Central Line L(53, 281) { 141, 344 }: Central Line L(141, 344) { 55, 678 }: Central Line L(55, 678) { 346, 594 }: Central Line L(346, 594) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_344 = ISOTOMIC CONJUGATE OF X(277) (0.6218, 0.2693) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) A B C X9 X1 X6 X2 X88 X53 X281 X141 X344 X55 X678 X346 X594 X45 (a, b, c) = (5, 6, 7) | AB = 1

X45 (X9-BETH CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2b + 2c - a : 2c + 2a - b : 2a + 2b - c\)
Barycentrics: \(a(2b + 2c - a) : b(2c + 2a - b) : c(2a + 2b - c)\)
Search Value (6, 9, 13): \(2.533082047975\)
▸ Linear Combinations1 combination
▸ Incident Central Lines8 lines

{1, 6}, {2, 88}, {53, 281}, {55, 678}, {141, 344}, {198, 1030}, {210, 968}, {346, 594}

▸ Functional Relations8 relations