X₆₆₅

CROSSDIFFERENCE OF X₂ AND X₁₁

X₆₆₅ = crossdifference of every pair of points on line {2, 11}

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

X₆₆₅ (CROSSDIFFERENCE OF X₂ AND X₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {101, 109}, {187, 237}

• Related Centers: X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER)), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₂₃₇ (-LINE CONJUGATE OF X₂)

Trilinears: \(a[(a - b)^{2}(a + b - c) - (c - a)^{2}(c + a - b)]\)

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

Search Value (6, 9, 13): \(-3.204118941621\)

▸ Linear Combinations1 combination

• X₆₆₅ = \(3\) X₁₆₃₅ - X₂₁₈₃₂, \(3\) X₁₆₃₈ - X₂₀₅₀₇, \(3\) X₁₆₃₈ - \(2\) X₂₀₅₂₀, \(2\) X₃₇₆₆ - \(3\) X₄₅₃₃₈, X₃₇₆₈ - \(3\) X₁₄₄₀₇, \(5\) X₄₆₉₉ - \(3\) X₂₁₄₃₃, \(5\) X₄₆₉₉ - \(9\) X₂₇₃₄₄, \(7\) X₄₇₅₁ - \(3\) X₂₁₆₀₆, \(3\) X₁₄₄₀₇ + X₂₁₁₄₃, X₂₁₄₃₃ - \(3\) X₂₇₃₄₄

▸ Incident Central Lines90 lines

{1, 4435}, {2, 3766}, {6, 22108}, {37, 900}, {39, 22092}, {101, 109}, {106, 2291}, {187, 237}, {241, 514}, {244, 866}, {292, 659}, {513, 3709}, {522, 21348}, {573, 2815}, {657, 20980}, {661, 2530}, {672, 14411}, {743, 761}, {784, 6590}, {798, 6371}, {802, 21191}, {834, 4832}, {911, 1438}, {918, 16728}, {926, 42079}, {1155, 9321}, {1213, 2511}, {1333, 42741}, {1362, 34905}, {1459, 3063}, {1639, 21894}, {1642, 2254}, {1734, 22229}, {1841, 39534}, {2092, 2642}, {2178, 39200}, {2195, 43929}, {2277, 28284}, {2345, 26078}, {2440, 32658}, {2483, 3733}, {2498, 3941}, {2516, 29226}, {2605, 21007}, {2609, 15586}, {3261, 17066}, {3287, 21173}, {3290, 26275}, {3512, 21391}, {3572, 6373}, {3700, 8714}, {3768, 6085}, {3798, 25098}, {3803, 4790}, {3835, 25084}, {3837, 40549}, {4017, 21127}, {4083, 4394}, {4139, 17458}, {4151, 4976}, {4374, 21225}, {4391, 22222}, {4449, 45755}, {4486, 24287}, {4524, 23655}, {4699, 21433}, {4751, 21606}, {4785, 45658}, {4985, 21960}, {6165, 21830}, {6363, 20979}, {9508, 30665}, {17263, 28779}, {17302, 27012}, {20678, 21003}, {21261, 25381}, {21742, 21758}, {21796, 24118}, {23744, 23798}, {24462, 41531}, {25594, 27293}, {26242, 44433}, {29350, 30234}, {30572, 42462}, {30764, 30836}, {31207, 31208}, {41163, 41190}, {41164, 41189}, {41165, 41186}, {41166, 41191}

▸ Functional Relations22 relations

• X₆₆₅ = midpoint of X_i and X_j for these {i,j}: {649, 3250}, {659, 876}, {798, 21123}, {3768, 21143}, {4374, 21225}

• X₆₆₅ = reflection of X_i in X_j for these {i,j}: {3261, 17066}, {3709, 6586}, {3837, 40549}, {4526, 37}, {20507, 20520}, {23744, 23798}, {45338, 2}

• X₆₆₅ = isogonal conjugate of X₆₆₆

• X₆₆₅ = isotomic conjugate of X₃₆₈₀₃

• X₆₆₅ = complement of X₃₇₆₆

• X₆₆₅ = Parry-circle inverse of X₅₀₉₈

• X₆₆₅ = tripolar centroid of X₁₀₀₂

• X₆₆₅ = X_i-complementary conjugate of X_j for these (i,j): {31, 38989}, {32, 35119}, {100, 20542}, {101, 20333}, {291, 21252}, {292, 116}, {660, 2887}, {692, 17793}, {813, 141}, {1252, 27854}, {1911, 11}, {1922, 1086}, {4557, 45162}, {4562, 626}, {4583, 21235}, {4584, 21240}, {5378, 21260}, {7077, 124}, {14598, 1015}, {17938, 6682}, {18265, 1146}, {18267, 39786}, {18268, 17761}, {18897, 6377}, {20964, 2679}, {23990, 27929}, {32739, 17755}, {34067, 10}, {36081, 21238}

• X₆₆₅ = X_i-Ceva conjugate of X_j for these (i,j): {2, 38989}, {6, 35505}, {7, 15615}, {56, 38363}, {100, 20455}, {101, 20662}, {105, 3271}, {241, 3675}, {292, 1015}, {651, 1362}, {659, 6373}, {660, 40730}, {876, 512}, {884, 20980}, {911, 7117}, {919, 6}, {927, 21746}, {1026, 20683}, {2254, 926}, {2283, 2223}, {2284, 672}, {2424, 663}, {5089, 17435}, {27918, 6165}, {34018, 4014}, {34067, 39}, {35185, 2175}, {37137, 34253}, {40519, 20860}, {42720, 518}, {43736, 3022}, {43760, 1357}

• X₆₆₅ = X_i-cross conjugate of X_j for these (i,j): {15615, 7}, {35505, 6}

• X₆₆₅ = crosspoint of X_i and X_j for these (i,j): {2, 660}, {6, 919}, {100, 2991}, {105, 651}, {110, 37128}, {241, 2283}, {518, 42720}, {649, 3572}, {672, 2284}, {694, 37137}, {1026, 18206}

• X₆₆₅ = crosssum of X_i and X_j for these (i,j): {2, 918}, {6, 659}, {100, 2284}, {105, 43929}, {190, 3570}, {294, 885}, {385, 3287}, {513, 3290}, {514, 3008}, {518, 650}, {522, 40869}, {523, 2238}, {812, 27942}, {926, 16588}, {1027, 18785}, {14942, 28132}

• X₆₆₅ = trilinear pole of line {15615, 35505}

• X₆₆₅ = crossdifference of every pair of points on line {2, 11}

• X₆₆₅ = tripolar centroid of X₁₀₀₂

• X₆₆₅ = polar conjugate of isogonal conjugate of X₂₃₂₂₅

• X₆₆₅ = perspector of hyperbola {A, B, C,X₆,X₇}}

• X₆₆₅ = X_i-cross conjugate of X_j for these (i,j): {15615, 7}, {35505, 6}

• X_i-isoconjugate of X_j for these (i,j): {1, 666}, {2, 36086}, {8, 36146}, {9, 927}, {31, 36803}, {41, 46135}, {55, 34085}, {57, 36802}, {75, 919}, {76, 32666}, {83, 35333}, {99, 18785}, {100, 673}, {101, 2481}, {105, 190}, {109, 36796}, {294, 664}, {312, 32735}, {344, 36041}, {514, 5377}, {646, 1416}, {650, 39293}, {651, 14942}, {658, 28071}, {660, 6654}, {662, 13576}, {668, 1438}, {692, 18031}, {885, 4564}, {898, 36816}, {934, 6559}, {1016, 1027}, {1024, 4998}, {1026, 6185}, {1292, 31638}, {1332, 36124}, {1462, 3699}, {1783, 31637}, {1814, 1897}, {2195, 4554}, {2398, 9503}, {3008, 39272}, {3112, 46163}, {3939, 34018}, {4441, 36138}, {4561, 8751}, {4614, 14625}, {6335, 36057}, {6632, 43921}, {7035, 43929}, {7045, 28132}, {9310, 14727}, {14947, 34906}, {20927, 35185}, {21615, 32724}, {23696, 46102}, {28420, 36111}

• X₆₆₅ = barycentric product X_i*X_j for these {i,j}: {1, 2254}, {6, 918}, {7, 926}, {11, 2283}, {42, 23829}, {55, 43042}, {58, 4088}, {81, 24290}, {100, 3675}, {104, 42758}, {105, 3126}, {241, 650}, {244, 1026}, {264, 23225}, {512, 30941}, {513, 518}, {514, 672}, {521, 1876}, {522, 1458}, {523, 3286}, {647, 15149}, {649, 3912}, {651, 17435}, {652, 5236}, {659, 22116}, {660, 38989}, {661, 18206}, {663, 9436}, {666, 35505}, {667, 3263}, {693, 2223}, {798, 18157}, {812, 3252}, {876, 8299}, {883, 3271}, {885, 1362}, {900, 34230}, {905, 5089}, {919, 35094}, {1015, 42720}, {1019, 3930}, {1022, 14439}, {1025, 2170}, {1027, 4712}, {1086, 2284}, {1459, 1861}, {1769, 36819}, {1818, 7649}, {2310, 41353}, {2340, 3676}, {2356, 4025}, {2428, 4904}, {3063, 40704}, {3261, 9454}, {3445, 4925}, {3572, 17755}, {3669, 3693}, {3717, 43924}, {3733, 3932}, {3766, 40730}, {3900, 34855}, {4238, 18210}, {4437, 43929}, {4778, 14626}, {6063, 8638}, {6591, 25083}, {7192, 20683}, {7199, 39258}, {8632, 40217}, {9309, 42341}, {9318, 34905}, {9455, 40495}, {15615, 46135}, {17094, 37908}, {17924, 20752}, {22383, 46108}, {23770, 34159}, {23773, 34071}, {32641, 42770}, {35293, 35348}

• X₆₆₅ = barycentric quotient X_i/X_j for these {i,j}: {2, 36803}, {6, 666}, {7, 46135}, {31, 36086}, {32, 919}, {55, 36802}, {56, 927}, {57, 34085}, {109, 39293}, {241, 4554}, {512, 13576}, {513, 2481}, {514, 18031}, {518, 668}, {560, 32666}, {604, 36146}, {649, 673}, {650, 36796}, {657, 6559}, {663, 14942}, {667, 105}, {672, 190}, {692, 5377}, {798, 18785}, {918, 76}, {926, 8}, {1026, 7035}, {1357, 43930}, {1362, 883}, {1397, 32735}, {1458, 664}, {1459, 31637}, {1642, 42722}, {1818, 4561}, {1876, 18026}, {1919, 1438}, {1964, 35333}, {1977, 43929}, {2223, 100}, {2254, 75}, {2283, 4998}, {2284, 1016}, {2340, 3699}, {2356, 1897}, {3051, 46163}, {3063, 294}, {3126, 3263}, {3248, 1027}, {3252, 4562}, {3263, 6386}, {3271, 885}, {3286, 99}, {3669, 34018}, {3675, 693}, {3693, 646}, {3768, 36816}, {3912, 1978}, {3930, 4033}, {3932, 27808}, {4088, 313}, {4832, 14625}, {5089, 6335}, {6184, 42720}, {8027, 43921}, {8299, 874}, {8632, 6654}, {8638, 55}, {8641, 28071}, {9309, 14727}, {9436, 4572}, {9454, 101}, {9455, 692}, {9502, 42719}, {14439, 24004}, {14936, 28132}, {15149, 6331}, {15615, 926}, {17435, 4391}, {17755, 27853}, {18157, 4602}, {18206, 799}, {20683, 3952}, {20752, 1332}, {20958, 35313}, {22116, 4583}, {22383, 1814}, {23225, 3}, {23829, 310}, {24290, 321}, {30941, 670}, {34159, 35574}, {34230, 4555}, {34855, 4569}, {35505, 918}, {37908, 36797}, {38989, 3766}, {39258, 1018}, {39686, 2284}, {40730, 660}, {42079, 1026}, {42720, 31625}, {42758, 3262}, {42771, 2804}, {43042, 6063}, {43929, 6185}

• X₆₆₅ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {649, 1960, 8658}, {649, 5029, 8632}, {649, 8632, 8659}, {650, 43060, 7180}, {657, 43924, 20980}, {1635, 14413, 1643}, {1635, 21828, 3310}, {1638, 20507, 20520}, {1960, 8659, 8632}, {5029, 8632, 1960}, {5638, 5639, 5098}, {8632, 8659, 8658}, {14407, 21143, 3768}, {21173, 21390, 3287}, {43047, 43050, 30725}