X₂₁₇

X₆-CEVA CONJUGATE OF X₅₁

X₂₁₇ = X₉₂-isoconjugate of X₉₅

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₁₇ (X₆-CEVA CONJUGATE OF X₅₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 6}, {54, 112}

• Related Centers: X₆ (SYMMEDIAN POINT), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₄ (ORTHOCENTER), X₅₄ (KOSNITA POINT), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT))

Trilinears: \((\sin^{3} A) \cos A \cos(B - C) : :\)

Barycentrics: \(a^{4} (a^{2} - b^{2} - c^{2}) \cdot (a^{2} b^{2} - b^{4} + a^{2} c^{2} + 2 b^{2} c^{2} - c^{4}) : :\)

Search Value (6, 9, 13): \(-0.102176669002\)

X₂₁₇ lies on the cubic K1088.

▸ Incident Central Lines60 lines

{3, 3289}, {4, 6}, {5, 1625}, {32, 184}, {39, 185}, {51, 3199}, {54, 112}, {83, 287}, {125, 1506}, {187, 13367}, {213, 20230}, {216, 5562}, {232, 389}, {263, 10790}, {394, 3785}, {574, 1204}, {577, 10984}, {578, 1968}, {648, 9291}, {1015, 1425}, {1404, 1409}, {1500, 3270}, {1562, 7765}, {1614, 1971}, {1691, 11674}, {1692, 5167}, {1899, 2548}, {1993, 20065}, {1994, 20088}, {2909, 20968}, {2965, 14533}, {3053, 19357}, {3172, 11402}, {3398, 17974}, {4173, 6752}, {4846, 15075}, {5007, 8779}, {5013, 10605}, {5038, 5622}, {5052, 6467}, {5058, 21640}, {5062, 21641}, {5889, 22240}, {6423, 19356}, {6424, 19355}, {6759, 10311}, {7736, 18909}, {7737, 19467}, {7747, 21659}, {7757, 9289}, {8571, 10254}, {10547, 14600}, {10986, 26882}, {12111, 26216}, {13330, 15073}, {13366, 14581}, {13754, 22416}, {15043, 15355}, {16502, 19349}, {18445, 23128}

▸ Functional Relations11 relations

• X₂₁₇ = isogonal conjugate of X₂₇₆

• X₂₁₇ = anticomplement of X₃₄₈₅₀

• X₂₁₇ = X_i-Ceva conjugate of X_j for these (i,j): {6, 51}, {216, 418}, {1625, 15451}, {1987, 237}

• X₂₁₇ = X_i-isoconjugate of X_j for these (i,j): {1, 276}, {54, 1969}, {63, 8795}, {75, 275}, {76, 2190}, {92, 95}, {264, 2167}, {304, 8884}, {326, 8794}, {561, 8882}, {811, 15412}, {933, 20948}, {1577, 18831}, {2148, 18022}, {2169, 18027}, {2616, 6331}, {14208, 16813}

• X₂₁₇ = crosspoint of X_i and X_j for these (i,j): {6, 184}, {51, 216}

• X₂₁₇ = crossdifference of every pair of points on line {340, 520}

• X₂₁₇ = crosssum of X_i and X_j for these (i,j): {2, 264}, {76, 7763}, {95, 275}

• X₂₁₇ = X₉₂-isoconjugate of X₉₅

• X₂₁₇ = barycentric product X_i*X_j for these {i,j}: {3, 51}, {4, 418}, {5, 184}, {6, 216}, {25, 5562}, {32, 343}, {48, 1953}, {52, 2351}, {53, 577}, {63, 2179}, {110, 15451}, {112, 17434}, {154, 8798}, {212, 1393}, {213, 16697}, {228, 18180}, {255, 2181}, {311, 14575}, {324, 14585}, {394, 3199}, {512, 23181}, {560, 18695}, {603, 7069}, {647, 1625}, {810, 2617}, {1092, 14569}, {1437, 21807}, {1576, 6368}, {1820, 2180}, {2200, 17167}, {3049, 14570}, {3078, 20574}, {3527, 26907}, {9247, 14213}, {13450, 23606}, {14587, 24862}, {17500, 20775}

• X₂₁₇ = barycentric quotient X_i/X_j for these {i,j}: {5, 18022}, {6, 276}, {25, 8795}, {32, 275}, {51, 264}, {53, 18027}, {184, 95}, {216, 76}, {343, 1502}, {418, 69}, {560, 2190}, {1501, 8882}, {1576, 18831}, {1625, 6331}, {1953, 1969}, {1974, 8884}, {2179, 92}, {2207, 8794}, {3049, 15412}, {3199, 2052}, {5562, 305}, {9247, 2167}, {9418, 19189}, {14574, 933}, {14575, 54}, {14585, 97}, {15451, 850}, {16697, 6385}, {17434, 3267}, {18695, 1928}, {23181, 670}

• X₂₁₇ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): (32, 184, 14585), (39, 185, 3269), (54, 112, 1970), (1614, 10312, 1971), (7592, 8743, 6)