X1814

INVERSE MIMOSA TRANSFORM OF X672

X1814 = reflection of X651 in X6
< 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) { 651, 6 }: Central Line L(651, 6) { 6, 7 }: Central Line L(6, 7) { 48, 77 }: Central Line L(48, 77) { 81, 105 }: Central Line L(81, 105) { 63, 212 }: Central Line L(63, 212) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_1814 = INVERSE MIMOSA TRANSFORM OF X(672) (0.8952, -0.0254) A B C X651 X6 X7 X48 X77 X81 X105 X63 X212 X1814 (a, b, c) = (5, 6, 7) | AB = 1

X1814 (INVERSE MIMOSA TRANSFORM OF X672) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(b + c - a \sec A) : :\)
Search Value (6, 9, 13): \(1.638929720984\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines9 lines

{6, 7}, {48, 77}, {63, 212}, {69, 219}, {81, 105}, {150, 1783}, {286, 648}, {518, 677}, {1438, 1449}

▸ Functional Relations4 relations