X1475

X1212-BETH CONJUGATE OF X1212

X1475 = crosssum of X2 and 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) { 6, 41 }: Central Line L(6, 41) { 39, 42 }: Central Line L(39, 42) { 58, 163 }: Central Line L(58, 163) { 57, 279 }: Central Line L(57, 279) { 71, 583 }: Central Line L(71, 583) { 1, 672 }: Central Line L(1, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_1 = INCENTER (0.5714, 0.2333) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1475 = -BETH CONJUGATE OF X(1212) (0.6083, 0.2874) A B C X1212 X6 X41 X39 X42 X58 X163 X57 X279 X71 X583 X1 X672 X1475 (a, b, c) = (5, 6, 7) | AB = 1

X1475 (X1212-BETH CONJUGATE OF X1212) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X1212
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.724099451163\)
▸ Incident Central Lines14 lines

{1, 672}, {6, 41}, {39, 42}, {57, 279}, {58, 163}, {71, 583}, {213, 1015}, {218, 999}, {354, 1212}, {579, 1449}, {607, 1398}, {649, 764}, {673, 1434}, {934, 1170}

▸ Functional Relations6 relations