X1213

ISOGONAL CONJUGATE OF X1171

X1213 is the isogonal conjugate of X1171.
< 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, 6 }: Centroid–Symmedian Line { 10, 37 }: Central Line L(10, 37) { 9, 46 }: Central Line L(9, 46) { 115, 121 }: Central Line L(115, 121) { 19, 429 }: Central Line L(19, 429) { 5, 573 }: Central Line L(5, 573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1171 = 1st SARAGOSSA POINT OF X(42) (0.6052, 0.2763) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_19 = CLAWSON POINT (0.6246, 0.4244) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) A B C X1171 X2 X6 X10 X37 X9 X46 X115 X121 X19 X429 X5 X573 X1213 (a, b, c) = (5, 6, 7) | AB = 1

X1213 (ISOGONAL CONJUGATE OF X1171) 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 \(f(a,b,c) = bc(b + c)(2a + b + c)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(2.855906858831\)
▸ Incident Central Lines14 lines

{2, 6}, {5, 573}, {9, 46}, {10, 37}, {19, 429}, {21, 1030}, {115, 121}, {140, 572}, {190, 1268}, {281, 860}, {440, 910}, {451, 1172}, {1100, 1125}, {1230, 1269}

▸ Functional Relations12 relations