X742

EVEN (- 1, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X742 lies on the line at infinity.
< 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) { 6, 75 }: Central Line L(6, 75) { 37, 141 }: Central Line L(37, 141) { 69, 192 }: Central Line L(69, 192) { 30, 511 }: Central Line L(30, 511) { 320, 335 }: Central Line L(320, 335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_743 = EVEN (- 1, 2) CIRCUMCIRCLE POINT (1.0002, 0.0008) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_742 = EVEN (- 1, 2) INFINITY POINT (0.1179, -0.2104) A B C X743 X6 X75 X37 X141 X69 X192 X30 X511 X320 X335 X742 (a, b, c) = (5, 6, 7) | AB = 1

X742 (EVEN (- 1, 2) INFINITY POINT) 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 \(f(a,b,c) = a ^{-2}(b^{2} + c^{2}) - a^{1}(b ^{-1} + c ^{-1})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines5 lines

{6, 75}, {30, 511}, {37, 141}, {69, 192}, {320, 335}

▸ Functional Relations2 relations