X961

ISOGONAL CONJUGATE OF X960

X961 is the isogonal conjugate of X960.
< 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) { 2, 12 }: Central Line L(2, 12) { 65, 81 }: Central Line L(65, 81) { 108, 429 }: Central Line L(108, 429) { 1, 572 }: Central Line L(1, 572) { 6, 959 }: Central Line L(6, 959) { 57, 1106 }: Central Line L(57, 1106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_1 = INCENTER (0.5714, 0.2333) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_959 = ISOGONAL CONJUGATE OF X(958) (0.6111, 0.3031) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1106 = TRILINEAR SQUARE OF X(56) (0.6507, 0.4375) X_961 = ISOGONAL CONJUGATE OF X(960) (0.6167, 0.3210) A B C X56 X65 X2 X12 X81 X108 X429 X1 X572 X6 X959 X57 X1106 X961 (a, b, c) = (5, 6, 7) | AB = 1

X961 (ISOGONAL CONJUGATE OF X960) 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 \(f(a,b,c) = 1/[(b + c - a)(b^{2} + c^{2} + ab + ac)]\)
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): \(0.319867802756\)
▸ Incident Central Lines8 lines

{1, 572}, {2, 12}, {6, 959}, {57, 1106}, {65, 81}, {105, 1104}, {108, 429}, {274, 1014}

▸ Functional Relations4 relations