X2073

INVERSE-IN-CIRCUMCIRCLE OF X27

X2073 = circumcircle-inverse of X27
< 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) circumcircle: Circumcircle of △ABC { 3, 27 }: Euler Line { 2, 3 }: Euler Line { 35, 270 }: Central Line L(35, 270) { 110, 916 }: Central Line L(110, 916) { 476, 917 }: Central Line L(476, 917) { 103, 1304 }: Central Line L(103, 1304) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_2 = CENTROID (0.5374, 0.2000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_916 = -CEVA CONJUGATE OF X(3) (0.0224, -0.0814) X_476 = TIXIER POINT (0.9824, 0.2685) X_917 = -CROSS CONJUGATE OF X(4) (0.9795, 0.2766) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_1304 = COLLINGS TRANSFORM OF X(403) (0.7822, 0.5273) X_2073 = INVERSE-IN-CIRCUMCIRCLE OF X(27) (0.7809, 0.8370) A B C X3 X27 X2 X35 X270 X110 X916 X476 X917 X103 X1304 X2073 (a, b, c) = (5, 6, 7) | AB = 1

X2073 (INVERSE-IN-CIRCUMCIRCLE OF X27) 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) is as noted just above X2070 using X = X27
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.427129500740\)
▸ Incident Central Lines6 lines

{2, 3}, {35, 270}, {103, 1304}, {110, 916}, {476, 917}, {675, 935}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X2073 has Shinagawa coefficients \((EF(R/|OX|)^{2} - (\$a\$\$bc\$ - abc)F{1 - (R/|OX|)^{2}}, -[(E + F) + \$bc\$]E(R/|OX|)^{2} + (\$a\$\$bc\$ - abc)F{1 - (R/|OX|)^{2}})\).