X3435
X8 -VERTEX CONJUGATE OF X8
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) { 24, 104 }: Central Line L(24, 104) { 8, 197 }: Central Line L(8, 197) { 48, 836 }: Central Line L(48, 836) { 3, 960 }: Central Line L(3, 960) { 56, 1452 }: Central Line L(56, 1452) { 603, 1193 }: Central Line L(603, 1193)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3436 = ISOGONAL CONJUGATE OF X(3435) (0.3491, -0.0877) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_8 = NAGEL POINT (0.4694, 0.1333) X_197 = -CEVA CONJUGATE OF X(6) (0.4333, -0.1633) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_836 = CROSSPOINT OF X(1) AND X(394) (0.5391, 0.0551) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1452 = -BETH CONJUGATE OF X(406) (0.6246, 0.4049) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.5959, 0.2573) X_3435 = -VERTEX CONJUGATE OF X(8) (0.5654, 0.9233)
A
B
C
X3436
X24
X104
X8
X197
X48
X836
X3
X960
X56
X1452
X603
X1193
X3435
(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) { 24, 104 }: Central Line L(24, 104) { 8, 197 }: Central Line L(8, 197) { 3, 960 }: Central Line L(3, 960) { 56, 1452 }: Central Line L(56, 1452) { 603, 1193 }: Central Line L(603, 1193) { 25, 2217 }: Central Line L(25, 2217)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3436 = ISOGONAL CONJUGATE OF X(3435) (0.3067, -0.1867) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6400, 0.4800) X_104 = ANTIPODE OF X(100) (0.8000, -0.4000) X_8 = NAGEL POINT (0.4400, 0.0800) X_197 = -CEVA CONJUGATE OF X(6) (0.4000, -0.7000) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5000, 0.1000) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6667, 0.3333) X_1452 = -BETH CONJUGATE OF X(406) (0.6400, 0.4800) X_603 = -CEVA CONJUGATE OF X(56) (0.6667, 0.0000) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.6364, 0.2273) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6400, 0.4800) X_2217 = -ISOCONJUGATE OF X(573) (0.6000, 0.7000) X_3435 = -VERTEX CONJUGATE OF X(8) (0.5000, 1.2500)
A
B
C
X3436
X24
X104
X8
X197
X3
X960
X56
X1452
X603
X1193
X25
X2217
X3435
(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) { 24, 104 }: Central Line L(24, 104) { 8, 197 }: Central Line L(8, 197) { 3, 960 }: Central Line L(3, 960) { 56, 1452 }: Central Line L(56, 1452) { 603, 1193 }: Central Line L(603, 1193) { 25, 2217 }: Central Line L(25, 2217)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3436 = ISOGONAL CONJUGATE OF X(3435) (0.3359, -0.1925) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6180, 0.4859) X_104 = ANTIPODE OF X(100) (0.7614, -0.4263) X_8 = NAGEL POINT (0.4499, 0.0817) X_197 = -CEVA CONJUGATE OF X(6) (0.4159, -0.7021) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5000, 0.1010) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6411, 0.3392) X_1452 = -BETH CONJUGATE OF X(406) (0.6180, 0.4859) X_603 = -CEVA CONJUGATE OF X(56) (0.6411, 0.0000) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.6149, 0.2298) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6180, 0.4859) X_2217 = -ISOCONJUGATE OF X(573) (0.5841, 0.7021) X_3435 = -VERTEX CONJUGATE OF X(8) (0.5000, 1.2371)
A
B
C
X3436
X24
X104
X8
X197
X3
X960
X56
X1452
X603
X1193
X25
X2217
X3435
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) { 24, 104 }: Central Line L(24, 104) { 8, 197 }: Central Line L(8, 197) { 48, 836 }: Central Line L(48, 836) { 3, 960 }: Central Line L(3, 960) { 56, 1452 }: Central Line L(56, 1452) { 603, 1193 }: Central Line L(603, 1193)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3436 = ISOGONAL CONJUGATE OF X(3435) (0.3342, -0.2189) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.5555, 0.1854) X_104 = ANTIPODE OF X(100) (0.6794, -0.8162) X_8 = NAGEL POINT (0.4024, 0.0200) X_197 = -CEVA CONJUGATE OF X(6) (0.5376, 1.2068) X_48 = CROSSPOINT OF X(1) AND X(63) (0.8073, -1.4298) X_836 = CROSSPOINT OF X(1) AND X(394) (0.5872, 0.0614) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.4957, 0.0289) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6494, 0.2495) X_1452 = -BETH CONJUGATE OF X(406) (0.7202, 0.0332) X_603 = -CEVA CONJUGATE OF X(56) (0.6002, 0.3540) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.6586, 0.1523) X_3435 = -VERTEX CONJUGATE OF X(8) (0.4856, 0.7502)
A
B
C
X3436
X24
X104
X8
X197
X48
X836
X3
X960
X56
X1452
X603
X1193
X3435
Kimberling (6, 9, 13) | AB = 1
X3435 (X8 -VERTEX CONJUGATE OF X8 ) 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
\(u : v : w\) =
X8 and
\(x : y : z\) =
X8 Barycentrics: \(a^{2}/[a^{4} + 2a^{2}bc - 2abc(b + c) - (b^{2} - c^{2})^{2}] : : (E. Danneels)\)
Search Value (6, 9, 13): \(-3.694044960961\)
▸ Incident Central Lines7 lines
{3 960 8 197 24 104 25 2217 48 836 56 1452 603 1193
▸ Functional Relations2 relations
