X440

COMPLEMENT OF X27

X440 is the complement of X27.
< 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, 27 }: Euler Line { 2, 3 }: Euler Line { 118, 122 }: Central Line L(118, 122) { 37, 226 }: Central Line L(37, 226) { 72, 306 }: Central Line L(72, 306) { 950, 1104 }: Central Line L(950, 1104) 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_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_122 = -OF-MEDIAL-TRIANGLE (0.5195, -0.0036) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_950 = CROSSPOINT OF X(8) AND X(29) (0.5621, 0.1961) X_1104 = CROSSPOINT OF X(1) AND X(28) (0.6311, 0.3042) X_440 = COMPLEMENT OF X(27) (0.4970, 0.0943) A B C Ma Mb Mc X2 X27 X3 X118 X122 X37 X226 X72 X306 X950 X1104 X440 (a, b, c) = (5, 6, 7) | AB = 1

X440 (COMPLEMENT OF X27) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(v + w) : ca(w + u) : ab(u + v)\), where \(u : v : w\) = X28; e.g., \(u(a,b,c) = (\tan A)/(b + c)\)
Barycentrics: \(v + w : w + u : u + v\)
Search Value (6, 9, 13): \(5.242466206828\)
▸ Incident Central Lines5 lines

{2, 3}, {37, 226}, {72, 306}, {118, 122}, {950, 1104}

▸ Functional Relations5 relations

Notes

As a point on the Euler line, X440 has Shinagawa coefficients \((\$bc\$ + E - F,-\$bc\$ - E - F)\)