X2398

GIBERT-SIMSON TRANSFORM OF X101

X2398 = cevapoint of X516 and X676
< 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, 2 }: Nagel Line { 100, 658 }: Central Line L(100, 658) { 666, 885 }: Central Line L(666, 885) { 677, 883 }: Central Line L(677, 883) { 644, 1783 }: Central Line L(644, 1783) { 765, 2397 }: Central Line L(765, 2397) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2424 = ISOGONAL CONJUGATE OF X(2398) (1.0916, 0.1371) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_885 = ISOTOMIC CONJUGATE OF X(883) (1.0518, 0.0256) X_677 = TRILINEAR POLE OF LINE X(3)X(101) (1.3200, 0.4790) X_883 = INTERSECTION OF LINES X(7)X(8) AND X(190)X(644) (1.5694, 1.4397) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_1783 = MIMOSA TRANSFORM OF X(1262) (0.4733, 0.5954) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_2397 = GIBERT-SIMSON TRANSFORM OF X(100) (4.6735, 3.5993) X_2398 = GIBERT-SIMSON TRANSFORM OF X(101) (1.4898, 1.1331) A B C X2424 X1 X2 X100 X658 X666 X885 X677 X883 X644 X1783 X765 X2397 X2398 (a, b, c) = (5, 6, 7) | AB = 1

X2398 (GIBERT-SIMSON TRANSFORM OF X101) 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 given just before X2394
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.594205669450\)

X2398 lies on the cubic K010.

▸ Incident Central Lines8 lines

{1, 2}, {59, 2406}, {100, 658}, {644, 1783}, {666, 885}, {677, 883}, {765, 2397}, {901, 2403}

▸ Functional Relations9 relations