X3654

X1-EXTRAVERSION OF {X1, X2, X3}

< 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) { 30, 40 }: Central Line L(30, 40) { 8, 376 }: Central Line L(8, 376) { 10, 381 }: Central Line L(10, 381) { 2, 392 }: Central Line L(2, 392) { 3, 519 }: Central Line L(3, 519) { 1, 549 }: Central Line L(1, 549) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_40 = BEVAN POINT (0.4286, -0.0292) X_8 = NAGEL POINT (0.4694, 0.1333) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_2 = CENTROID (0.5374, 0.2000) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1 = INCENTER (0.5714, 0.2333) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_3654 = -EXTRAVERSION OF {X(1), X(2), X(3)} (0.4660, 0.0687) A B C X30 X40 X8 X376 X10 X381 X2 X392 X3 X519 X1 X549 X3654 (a, b, c) = (5, 6, 7) | AB = 1

X3654 (X1-EXTRAVERSION OF {X1, X2, X3}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{4}+3 (b+c) a^{3}-2 (b^{2}+3 b c+c^{2}) a^{2}-3 (b^{2}-c^{2}) \cdot (b-c) a+(b^{2}-c^{2})^{2} : :\)
Search Value (6, 9, 13): \(7.721423177228\)
▸ Linear Combinations1 combination
▸ Incident Central Lines16 lines

{1, 549}, {2, 392}, {3, 519}, {8, 376}, {10, 381}, {30, 40}, {63, 1145}, {165, 952}, {495, 2093}, {515, 3534}, {542, 3416}, {547, 1698}, {551, 1482}, {962, 3545}, {1385, 3241}, {1836, 3245}