X2948

EXCENTRAL-ISOGONAL CONJUGATE OF X30

X2948 is the excentral-isogonal conjugate of X30.
< 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) { 1, 110 }: Central Line L(1, 110) { 1, 60 }: Central Line L(1, 60) { 3, 191 }: Central Line L(3, 191) { 74, 165 }: Central Line L(74, 165) { 146, 516 }: Central Line L(146, 516) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (-0.0682, 0.8624) A B C X1 X110 X60 X3 X191 X74 X165 X146 X516 X2948 (a, b, c) = (5, 6, 7) | AB = 1

X2948 (EXCENTRAL-ISOGONAL CONJUGATE OF X30) 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) is as described just before X2883
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.124817438746\)

X2948 lies on the Bevan circle.

▸ Incident Central Lines20 lines

{1, 60}, {3, 191}, {6, 1718}, {40, 2940}, {74, 165}, {80, 2607}, {113, 1699}, {125, 1698}, {146, 516}, {399, 517}, {518, 2930}, {758, 1325}, {912, 2931}, {1046, 1054}, {1282, 2774}, {1498, 2778}, {2100, 2574}, {2101, 2575}, {2772, 2938}, {2779, 2939}

▸ Functional Relations3 relations