X3433
X7 -VERTEX CONJUGATE OF X7
5, 6, 7
3, 4, 5
Kepler
Kimberling
< 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) { 104, 378 }: Central Line L(104, 378) { 3, 518 }: Central Line L(3, 518) { 48, 672 }: Central Line L(48, 672) { 7, 1486 }: Central Line L(7, 1486) { 692, 1037 }: Central Line L(692, 1037) { 56, 1876 }: Central Line L(56, 1876)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2175 = -ISOCONJUGATE OF X(85) (0.6102, 0.2574) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5798, 0.2866) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1876 = ZOSMA TRANSFORM OF X(516) (0.6639, 0.6754) X_3433 = -VERTEX CONJUGATE OF X(7) (0.6221, 0.2471)
A
B
C
X2175
X6
X104
X378
X3
X518
X48
X672
X7
X1486
X692
X1037
X56
X1876
X3433
(a, b, c) = (5, 6, 7) | AB = 1
< 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) { 104, 378 }: Central Line L(104, 378) { 3, 518 }: Central Line L(3, 518) { 48, 672 }: Central Line L(48, 672) { 7, 1486 }: Central Line L(7, 1486) { 692, 1037 }: Central Line L(692, 1037) { 56, 1876 }: Central Line L(56, 1876)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2175 = -ISOCONJUGATE OF X(85) (0.6609, 0.2174) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_104 = ANTIPODE OF X(100) (0.8000, -0.4000) X_378 = REFLECTION OF X(22) IN X(3) (0.6400, 0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9533, 0.5666) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5714, 0.0000) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.3913, 1.3043) X_7 = GERGONNE POINT (0.6218, 0.2618) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.6000, 0.2833) X_692 = -CEVA CONJUGATE OF X(101) (0.4000, 0.5000) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.6111, 0.2778) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_1876 = ZOSMA TRANSFORM OF X(516) (0.6400, 0.4800) X_3433 = -VERTEX CONJUGATE OF X(7) (0.6923, 0.1923)
A
B
C
X2175
X6
X104
X378
X3
X518
X48
X672
X7
X1486
X692
X1037
X56
X1876
X3433
(a, b, c) = (3, 4, 5) | AB = 1
< 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) { 104, 378 }: Central Line L(104, 378) { 3, 518 }: Central Line L(3, 518) { 48, 672 }: Central Line L(48, 672) { 7, 1486 }: Central Line L(7, 1486) { 692, 1037 }: Central Line L(692, 1037) { 56, 1876 }: Central Line L(56, 1876)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2175 = -ISOCONJUGATE OF X(85) (0.6360, 0.2201) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_104 = ANTIPODE OF X(100) (0.7614, -0.4263) X_378 = REFLECTION OF X(22) IN X(3) (0.6180, 0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9071, 0.6040) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5599, 0.0000) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.3003, 1.4042) X_7 = GERGONNE POINT (0.6026, 0.2652) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5841, 0.2862) X_692 = -CEVA CONJUGATE OF X(101) (0.4159, 0.5000) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5936, 0.2822) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_1876 = ZOSMA TRANSFORM OF X(516) (0.6180, 0.4859) X_3433 = -VERTEX CONJUGATE OF X(7) (0.6635, 0.1965)
A
B
C
X2175
X6
X104
X378
X3
X518
X48
X672
X7
X1486
X692
X1037
X56
X1876
X3433
Kepler (1, √φ, φ) | AB = 1
< 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) { 104, 378 }: Central Line L(104, 378) { 3, 518 }: Central Line L(3, 518) { 48, 672 }: Central Line L(48, 672) { 7, 1486 }: Central Line L(7, 1486) { 692, 1037 }: Central Line L(692, 1037) { 56, 1876 }: Central Line L(56, 1876)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2175 = -ISOCONJUGATE OF X(85) (0.7094, 0.1115) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_104 = ANTIPODE OF X(100) (0.6794, -0.8162) X_378 = REFLECTION OF X(22) IN X(3) (0.1672, -3.0347) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_518 = ISOGONAL CONJUGATE OF X(105) (1.0454, 0.5168) X_48 = CROSSPOINT OF X(1) AND X(63) (0.8073, -1.4298) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (0.9049, 0.5974) X_7 = GERGONNE POINT (0.6288, 0.2114) X_1486 = PERSPECTOR OF TANGENTIAL AND INTOUCH TRIANGLES (0.5849, 0.2406) X_692 = -CEVA CONJUGATE OF X(101) (0.5270, 0.3006) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.6253, 0.2291) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_1876 = ZOSMA TRANSFORM OF X(516) (0.6292, 0.2676) X_3433 = -VERTEX CONJUGATE OF X(7) (0.8783, 0.0450)
A
B
C
X2175
X6
X104
X378
X3
X518
X48
X672
X7
X1486
X692
X1037
X56
X1876
X3433
Kimberling (6, 9, 13) | AB = 1
X3433 (X7 -VERTEX CONJUGATE OF X7 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a/[a^{2}vwyz - ux(bw + cv)(bz + cy)] : :\) , where
\(u : v : w\) =
X7 and
\(x : y : z\) =
X7 Barycentrics: \(a^{2}/[a^{3} - a^{2}b - a^{2}c + ab^{2} + ac^{2} - (b + c)(b - c)^{2}] : : (E. Danneels)\)
Search Value (6, 9, 13): \(0.494948239438\)
▸ Incident Central Lines8 lines
{3 518 7 1486 48 672 56 1876 104 378 603 1458 692 1037 1437 1780
▸ Functional Relations2 relations
