X1449

{X1,X6}-HARMONIC CONJUGATE OF X9

X1449 is the {X1,X6}-harmonic conjugate of X9.
< 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) { 1, 6 }: Incenter–Symmedian Line { 57, 77 }: Central Line L(57, 77) { 65, 380 }: Central Line L(65, 380) { 40, 572 }: Central Line L(40, 572) { 32, 988 }: Central Line L(32, 988) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_40 = BEVAN POINT (0.4286, -0.0292) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_988 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(39) (0.5598, 0.2120) X_1449 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(9) (0.5830, 0.2470) A B C X9 X1 X6 X57 X77 X65 X380 X40 X572 X32 X988 X1449 (a, b, c) = (5, 6, 7) | AB = 1

X1449 ({X1,X6}-HARMONIC CONJUGATE OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(3a + b + c : 3b + c + a : 3c + a + b\)
Barycentrics: \(a(3a + b + c) : b(3b + c + a) : c(3c + a + b)\)
Search Value (6, 9, 13): \(1.396125022560\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a + s : b + s : c + s\)

▸ Incident Central Lines16 lines

{1, 6}, {7, 1419}, {32, 988}, {34, 1172}, {40, 572}, {43, 1051}, {57, 77}, {65, 380}, {87, 1045}, {198, 999}, {579, 1475}, {610, 942}, {894, 1278}, {966, 1125}, {1400, 1420}, {1442, 1445}

▸ Functional Relations5 relations