X752

EVEN (0, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X752 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) { 2, 31 }: Central Line L(2, 31) { 10, 44 }: Central Line L(10, 44) { 1, 320 }: Central Line L(1, 320) { 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_753 = EVEN (0, 3) CIRCUMCIRCLE POINT (0.9725, -0.0907) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_1 = INCENTER (0.5714, 0.2333) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_752 = EVEN (0, 3) INFINITY POINT (0.9166, 0.6478) A B C X753 X2 X31 X10 X44 X1 X320 X30 X511 X752 (a, b, c) = (5, 6, 7) | AB = 1

X752 (EVEN (0, 3) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a ^{-1}(b^{3} + c^{3}) - a^{2}(b^{0} + c^{0}) : :\)
Barycentrics: \(2 a^{3} - b^{3} - c^{3} : :\)
▸ Incident Central Lines4 lines

{1, 320}, {2, 31}, {10, 44}, {30, 511}

▸ Functional Relations3 relations