X2397

GIBERT-SIMSON TRANSFORM OF X100

X2397 = trilinear pole of line X119X517 (the Simson line of X100)
< 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) { 2, 37 }: Central Line L(2, 37) { 190, 644 }: Central Line L(190, 644) { 522, 1026 }: Central Line L(522, 1026) { 666, 2402 }: Central Line L(666, 2402) { 765, 2398 }: Central Line L(765, 2398) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2423 = ISOGONAL CONJUGATE OF X(2397) (1.0250, 0.1225) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_1026 = INTERSECTION OF LINES X(1)X(2) AND X(100)X(101) (4.1429, 3.7326) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_2402 = GIBERT-SIMSON TRANSFORM OF X(105) (0.9981, 0.0461) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_2398 = GIBERT-SIMSON TRANSFORM OF X(101) (1.4898, 1.1331) X_2397 = GIBERT-SIMSON TRANSFORM OF X(100) (4.6735, 3.5993) A B C X2423 X2 X37 X190 X644 X522 X1026 X666 X2402 X765 X2398 X2397 (a, b, c) = (5, 6, 7) | AB = 1

X2397 (GIBERT-SIMSON TRANSFORM OF X100) 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): \(-9.286277361330\)

X2397 lies on the cubic K010.

▸ Incident Central Lines5 lines

{2, 37}, {190, 644}, {522, 1026}, {666, 2402}, {765, 2398}

▸ Functional Relations3 relations