X₁₃₃₃

POINT ALULA

X₁₃₃₃ = X₃₁-cross conjugate of X₅₈

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

X₁₃₃₃ (POINT ALULA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {21, 37}

• Related Centers: X₃₂₁ (ISOTOMIC CONJUGATE OF X₈₁), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₂₁ (SCHIFFLER POINT), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID)

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

Search Value (6, 9, 13): \(0.397870854156\)

▸ Incident Central Lines131 lines

{2, 18744}, {3, 6}, {9, 609}, {19, 2217}, {21, 37}, {27, 3772}, {28, 1104}, {31, 48}, {36, 16470}, {44, 1778}, {45, 4877}, {47, 22134}, {53, 7511}, {56, 608}, {65, 1950}, {81, 593}, {86, 3662}, {99, 713}, {100, 21858}, {104, 112}, {110, 739}, {141, 5337}, {163, 9456}, {213, 2174}, {219, 1780}, {261, 27164}, {272, 379}, {286, 16732}, {292, 4628}, {314, 19623}, {321, 17587}, {333, 4386}, {346, 17539}, {385, 3770}, {536, 16046}, {594, 5291}, {595, 16685}, {603, 604}, {662, 18274}, {692, 1911}, {741, 825}, {759, 5341}, {849, 1437}, {859, 2178}, {872, 18266}, {896, 3958}, {910, 5324}, {940, 16368}, {963, 2332}, {992, 27660}, {1010, 4426}, {1014, 1418}, {1043, 17299}, {1086, 17189}, {1171, 28625}, {1178, 3863}, {1191, 2255}, {1193, 22054}, {1213, 5277}, {1396, 1427}, {1399, 1409}, {1400, 1415}, {1407, 1412}, {1436, 2299}, {1449, 7031}, {1575, 13588}, {1627, 5276}, {1766, 15952}, {1790, 2221}, {1801, 2327}, {1811, 5546}, {1817, 3752}, {1901, 13442}, {1931, 4469}, {1951, 2264}, {1977, 17961}, {2160, 3125}, {2162, 21769}, {2197, 5172}, {2241, 4658}, {2242, 4653}, {2256, 2328}, {2262, 18191}, {2268, 10457}, {2269, 22361}, {2276, 4184}, {2277, 4225}, {2311, 3862}, {2345, 11115}, {2361, 22074}, {2423, 7252}, {2699, 2715}, {2991, 4558}, {3290, 4228}, {3330, 28381}, {3454, 24935}, {3739, 26643}, {3998, 4641}, {4000, 14953}, {4234, 17281}, {4567, 5381}, {4749, 23868}, {5358, 16583}, {5563, 16488}, {5839, 16704}, {7735, 26118}, {8069, 22132}, {8822, 17276}, {9341, 19297}, {10315, 21866}, {10789, 18194}, {11102, 16974}, {11320, 18147}, {12194, 18170}, {12610, 17197}, {13728, 17398}, {16047, 17263}, {16050, 17279}, {16054, 17278}, {16350, 19701}, {16580, 17171}, {16706, 21997}, {16917, 25457}, {16973, 18206}, {17052, 24890}, {17053, 21773}, {17187, 21764}, {18697, 24335}, {19308, 24530}, {19785, 26830}, {21353, 21833}

▸ Functional Relations14 relations

• X₁₃₃₃ = isogonal conjugate of X₃₂₁

• X₁₃₃₃ = isotomic conjugate of X₂₇₈₀₁

• X₁₃₃₃ = complement of X₂₁₂₈₇

• X₁₃₃₃ = anticomplement of X₂₁₂₄₅

• X₁₃₃₃ = X_i-Ceva conjugate of X_j for these (i,j): (593, 58), (1169, 6), (1175, 184)

• X₁₃₃₃ = X₃₁-cross conjugate of X₅₈

• X₁₃₃₃ = cevapoint of X₃₁ and X₃₂

• X₁₃₃₃ = crosspoint of X_i and X_j for these (i,j): (28, 81), (58, 1412), (593, 849)

• X₁₃₃₃ = crosssum of X_i and X_j for (i,j) = (37,72), (594,1089)

• X₁₃₃₃ = trilinear pole of line X₆₆₇X₈₃₈

• X₁₃₃₃ = X₉₂-isoconjugate of X₇₂

• X₁₃₃₃ = X₁₀₀-isoconjugate of X₁₅₇₇

• X₁₃₃₃ = perspector of ABC and unary cofactor triangle of Gemini triangle 21

• X₁₃₃₃ = perspector of ABC and unary cofactor triangle of Gemini triangle 27