X1215

ISOGONAL CONJUGATE OF X1178

X1215 is the isogonal conjugate of X1178.
< 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) { 42, 321 }: Central Line L(42, 321) { 10, 12 }: Central Line L(10, 12) { 2, 38 }: Central Line L(2, 38) { 43, 75 }: Central Line L(43, 75) { 1, 312 }: Central Line L(1, 312) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2 = CENTROID (0.5374, 0.2000) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1 = INCENTER (0.5714, 0.2333) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) A B C X42 X321 X10 X12 X2 X38 X43 X75 X1 X312 X1215 (a, b, c) = (5, 6, 7) | AB = 1

X1215 (ISOGONAL CONJUGATE OF X1178) 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 \(f(a,b,c) = bc(b + c)(a^{2} + bc)\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(2.728253808729\)
▸ Incident Central Lines9 lines

{1, 312}, {2, 38}, {10, 12}, {37, 714}, {42, 321}, {43, 75}, {171, 385}, {190, 846}, {964, 976}

▸ Functional Relations8 relations