X739

EVEN (- 1, 0) CIRCUMCIRCLE POINT

X739 = trilinear pole of line X6X667
< 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, 100 }: Central Line L(6, 100) { 31, 101 }: Central Line L(31, 101) { 81, 99 }: Central Line L(81, 99) { 109, 604 }: Central Line L(109, 604) { 108, 608 }: Central Line L(108, 608) { 813, 902 }: Central Line L(813, 902) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_99 = STEINER POINT (0.1109, 0.4322) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (1.0101, 0.0884) A B C X536 X6 X100 X31 X101 X81 X99 X109 X604 X108 X608 X813 X902 X739 (a, b, c) = (5, 6, 7) | AB = 1

X739 (EVEN (- 1, 0) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a^{-2}(b^{0} + c^{0}) - a ^{-1}(b ^{-1} + c ^{-1})] : :\)
Search Value (6, 9, 13): \(-0.398312135219\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a/(2 b c - c a - a b) : :\)

X739 lies on the circumcircle.

▸ Incident Central Lines6 lines

{6, 100}, {31, 101}, {81, 99}, {108, 608}, {109, 604}, {813, 902}

▸ Functional Relations8 relations