X404

{X2,X3}-HARMONIC CONJUGATE OF X21

X404 is the {X2,X3}-harmonic conjugate of X21. For a list of harmonic conjugates of X404, click Tables at the top of this page.
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 320 }: Central Line L(2, 320) { 2, 3 }: Euler Line { 10, 36 }: Central Line L(10, 36) { 8, 56 }: Central Line L(8, 56) { 1, 88 }: Central Line L(1, 88) { 57, 78 }: Central Line L(57, 78) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) A B C Ma Mb Mc X2 X320 X3 X10 X36 X8 X56 X1 X88 X57 X78 X404 (a, b, c) = (5, 6, 7) | AB = 1

X404 ({X2,X3}-HARMONIC CONJUGATE OF X21) 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 \(f(a,b,c) = bc(a + b + c) - a(b^{2} + c^{2} - a^{2})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = abc(a + b + c) - a^{2}(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(1.885271305061\)
▸ Incident Central Lines18 lines

{1, 88}, {2, 3}, {8, 56}, {10, 36}, {31, 978}, {46, 997}, {57, 78}, {60, 662}, {63, 936}, {69, 1014}, {81, 386}, {104, 355}, {108, 318}, {145, 999}, {149, 496}, {603, 651}, {612, 988}, {976, 982}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X404 has Shinagawa coefficients \((abc \$a\$ - 2S^{2}, 2S^{2})\).