X3964

X1609com[INVERSE(n(TANGENTIAL TRIANGLE))]

X3964 = X92-isoconjugate of X2207
< 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) circumcircle: Circumcircle of △ABC { 3, 69 }: Central Line L(3, 69) { 95, 183 }: Central Line L(95, 183) { 25, 317 }: Central Line L(25, 317) { 394, 577 }: Central Line L(394, 577) { 264, 1105 }: Central Line L(264, 1105) { 99, 1294 }: Central Line L(99, 1294) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_317 = ISOTOMIC CONJUGATE OF X(68) (0.6796, 0.5070) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_1105 = CEVAPOINT OF X(3) AND X(4) (0.5529, 0.3087) X_99 = STEINER POINT (0.1109, 0.4322) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4267, -0.4030) X_3964 = com[INVERSE(n(TANGENTIAL TRIANGLE))] (0.2717, 0.0068) A B C X3 X69 X95 X183 X25 X317 X394 X577 X264 X1105 X99 X1294 X3964 (a, b, c) = (5, 6, 7) | AB = 1

X3964 (X1609com[INVERSE(n(TANGENTIAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(t(A,B,C) : t(B,C,A) : t(C,A,B)\), where \(t(A,B,C) = \cot^{2} A \cos A\) (Peter Moses, 1/13/2012)
Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{2} - c^{2} - a^{2})^{3}\)
Search Value (6, 9, 13): \(5.756155510596\)
▸ Incident Central Lines17 lines

{3, 69}, {25, 317}, {95, 183}, {99, 1294}, {159, 1634}, {253, 2071}, {264, 1105}, {326, 1259}, {340, 3515}, {394, 577}, {491, 1584}, {492, 1583}, {524, 1609}, {648, 1033}, {1073, 2063}, {1270, 1599}, {1271, 1600}

▸ Functional Relations3 relations