X875

ISOGONAL CONJUGATE OF X874

X875 is the isogonal conjugate of X874.
< 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, 512 }: Central Line L(1, 512) { 42, 649 }: Central Line L(42, 649) { 31, 669 }: Central Line L(31, 669) { 213, 667 }: Central Line L(213, 667) { 291, 659 }: Central Line L(291, 659) { 295, 926 }: Central Line L(295, 926) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_874 = INTERSECTION OF LINES X(1)X(75) AND X(99)X(670) (-2.0525, -2.1172) X_1 = INCENTER (0.5714, 0.2333) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_926 = CROSSDIFFERENCE OF X(6) AND X(7) (0.0512, -0.1286) X_875 = ISOGONAL CONJUGATE OF X(874) (0.9992, -0.0257) A B C X874 X1 X512 X42 X649 X31 X669 X213 X667 X291 X659 X295 X926 X875 (a, b, c) = (5, 6, 7) | AB = 1

X875 (ISOGONAL CONJUGATE OF X874) 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 \(f(a,b,c) = a^{2}u(bv - cw)/(a^{2}u^{2} - bcvw)\),\(u : v : w\) = X1
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.050859622864\)
▸ Incident Central Lines6 lines

{1, 512}, {31, 669}, {42, 649}, {213, 667}, {291, 659}, {295, 926}

▸ Functional Relations4 relations