X2979

CENTROID OF DUAL OF THE ORTHIC TRIANGLE

X2979 is the centroid of dual of the orthic triangle.
< 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) { 568, 549 }: Central Line L(568, 549) { 2, 51 }: Central Line L(2, 51) { 3, 54 }: Central Line L(3, 54) { 22, 110 }: Central Line L(22, 110) { 66, 69 }: Central Line L(66, 69) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_568 = ORTHOHARMONIC OF X(50) (0.6437, 0.3393) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_2 = CENTROID (0.5374, 0.2000) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_54 = KOSNITA POINT (0.5880, 0.2176) X_22 = EXETER POINT (0.4143, -0.1221) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE (0.3937, -0.0373) A B C X568 X549 X2 X51 X3 X54 X22 X110 X66 X69 X2979 (a, b, c) = (5, 6, 7) | AB = 1

X2979 (CENTROID OF DUAL OF THE ORTHIC TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{4} + c^{4} + b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.646855212051\)
▸ Incident Central Lines19 lines

{2, 51}, {3, 54}, {4, 1216}, {6, 1627}, {22, 110}, {52, 631}, {66, 69}, {182, 1994}, {184, 323}, {343, 858}, {476, 2706}, {549, 568}, {805, 2857}, {930, 1298}, {991, 1779}, {1160, 1584}, {1161, 1583}, {1501, 2076}, {2888, 2889}

▸ Functional Relations8 relations