X943

ISOGONAL CONJUGATE OF X942

X943 is the isogonal conjugate of X942.
< 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) { 3, 7 }: Central Line L(3, 7) { 4, 12 }: Central Line L(4, 12) { 21, 72 }: Central Line L(21, 72) { 35, 79 }: Central Line L(35, 79) { 1, 201 }: Central Line L(1, 201) { 28, 228 }: Central Line L(28, 228) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_4 = ORTHOCENTER (0.6122, 0.3958) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_1 = INCENTER (0.5714, 0.2333) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_943 = ISOGONAL CONJUGATE OF X(942) (0.5528, 0.2043) A B C X942 X3 X7 X4 X12 X21 X72 X35 X79 X1 X201 X28 X228 X943 (a, b, c) = (5, 6, 7) | AB = 1

X943 (ISOGONAL CONJUGATE OF X942) 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 \(f(a,b,c) = 1/[2abc + (b + c)(a - b + c)(a + b - c)]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(2.303063519133\)
▸ Incident Central Lines12 lines

{1, 201}, {3, 7}, {4, 12}, {8, 405}, {21, 72}, {28, 228}, {35, 79}, {80, 950}, {100, 442}, {500, 651}, {968, 1039}, {1001, 1058}

▸ Functional Relations5 relations