X729

EVEN (- 2, 0) CIRCUMCIRCLE POINT

X729 = Λ(X2, X39)
< 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, 99 }: Central Line L(6, 99) { 32, 110 }: Central Line L(32, 110) { 100, 213 }: Central Line L(100, 213) { 83, 689 }: Central Line L(83, 689) { 187, 805 }: Central Line L(187, 805) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_99 = STEINER POINT (0.1109, 0.4322) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) A B C X538 X6 X99 X32 X110 X100 X213 X83 X689 X187 X805 X729 (a, b, c) = (5, 6, 7) | AB = 1

X729 (EVEN (- 2, 0) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a^{-3}(b^{0} + c^{0}) - a ^{-1}(b^{-2} + c ^{-2})]\)
Search Value (6, 9, 13): \(-0.543706715408\)
▸ Alternate Coordinates1 form

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

X729 lies on the circumcircle.

▸ Incident Central Lines5 lines

{6, 99}, {32, 110}, {83, 689}, {100, 213}, {187, 805}

▸ Functional Relations11 relations