X758

EVEN (1, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X758 lies on the line at infinity.
< 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, 21 }: Central Line L(1, 21) { 10, 12 }: Central Line L(10, 12) { 8, 79 }: Central Line L(8, 79) { 46, 78 }: Central Line L(46, 78) { 36, 214 }: Central Line L(36, 214) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_8 = NAGEL POINT (0.4694, 0.1333) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) A B C X759 X1 X21 X10 X12 X8 X79 X46 X78 X36 X214 X30 X511 X758 (a, b, c) = (5, 6, 7) | AB = 1

X758 (EVEN (1, 3) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{0}(b^{3} + c^{3}) - a^{2}(b^{1} + c^{1})\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((b + c) \cot A - b \cot B - c \cot C : :\)

  • Trilinears: \((b + c) (b^{2} + c^{2} - a^{2} - bc) : :\)

▸ Incident Central Lines12 lines

{1, 21}, {8, 79}, {10, 12}, {30, 511}, {36, 214}, {46, 78}, {57, 997}, {100, 484}, {354, 392}, {386, 986}, {942, 960}, {982, 995}

▸ Functional Relations11 relations