X443

COMPLEMENT OF X452

X443 is the complement of X452.
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 452 }: Euler Line { 2, 3 }: Euler Line { 10, 57 }: Central Line L(10, 57) { 7, 72 }: Central Line L(7, 72) { 1, 142 }: Central Line L(1, 142) { 69, 274 }: Central Line L(69, 274) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_452 = -HIRST INVERSE OF X(449) (0.5268, 0.1722) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_7 = GERGONNE POINT (0.5903, 0.2769) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_443 = COMPLEMENT OF X(452) (0.5427, 0.2138) A B C Ma Mb Mc X2 X452 X3 X10 X57 X7 X72 X1 X142 X69 X274 X443 (a, b, c) = (5, 6, 7) | AB = 1

X443 (COMPLEMENT OF X452) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(v + w) : ca(w + u) : ab(u + v)\), where \(u : v : w\) = X380
Barycentrics: \(v + w : w + u : u + v\)
Search Value (6, 9, 13): \(2.325398501421\)
▸ Incident Central Lines77 lines

{1, 142}, {2, 3}, {6, 4340}, {7, 72}, {8, 942}, {9, 4292}, {10, 57}, {12, 1466}, {56, 3925}, {69, 274}, {78, 3487}, {141, 5800}, {153, 5789}, {226, 936}, {278, 1038}, {329, 5044}, {355, 5768}, {386, 5712}, {387, 940}, {392, 962}, {497, 1125}, {579, 966}, {610, 5750}, {750, 5230}, {908, 5714}, {938, 3419}, {946, 6282}, {948, 1448}, {956, 3600}, {958, 3826}, {960, 4295}, {965, 5746}, {997, 3485}, {1001, 4294}, {1058, 3434}, {1119, 1441}, {1210, 5437}, {1376, 3085}, {1453, 3008}, {1478, 1698}, {1479, 3624}, {1770, 5698}, {2093, 5837}, {2095, 5690}, {2886, 3086}, {2999, 5717}, {3333, 4847}, {3358, 5817}, {3436, 5744}, {3475, 3811}, {3587, 5250}, {3617, 5708}, {3618, 5138}, {3634, 5229}, {3697, 5815}, {3698, 5252}, {3812, 5794}, {3876, 5905}, {3911, 5705}, {3916, 5273}, {3940, 6147}, {4299, 5251}, {4302, 5259}, {4304, 5436}, {4317, 5258}, {4355, 5223}, {4423, 6284}, {4680, 6533}, {5080, 5122}, {5175, 5722}, {5219, 6700}, {5275, 5286}, {5440, 5703}, {5587, 6245}, {5657, 5709}, {5927, 6223}, {6256, 6705}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X443 has Shinagawa coefficients \((abc \$a\$, S^{2})\).