X2169

X2-ISOCONJUGATE OF X53

X2169 = X2167-Ceva conjugate of X2148
< 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) { 36, 54 }: Central Line L(36, 54) { 47, 48 }: Central Line L(47, 48) { 1, 1748 }: Central Line L(1, 1748) { 336, 1930 }: Central Line L(336, 1930) { 821, 1784 }: Central Line L(821, 1784) { 921, 2168 }: Central Line L(921, 2168) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2167 = -ISOCONJUGATE OF X(51) (0.5550, 0.1860) X_2148 = -ISOCONJUGATE OF X(5) (0.6157, 0.2500) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_54 = KOSNITA POINT (0.5880, 0.2176) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_1 = INCENTER (0.5714, 0.2333) X_1748 = MIMOSA TRANSFORM OF X(264) (0.6706, 0.5179) X_336 = ISOTOMIC CONJUGATE OF X(240) (0.7020, -0.0409) X_1930 = BICENTRIC SUM OF PU(14) (0.4644, 0.1374) X_821 = ISOGONAL CONJUGATE OF X(820) (0.5996, 0.4597) X_1784 = MIMOSA TRANSFORM OF X(1294) (0.6867, 0.8743) X_921 = ISOGONAL CONJUGATE OF X(920) (7.0160, 1.3242) X_2168 = -ISOCONJUGATE OF X(52) (-0.1206, -0.0284) X_2169 = -ISOCONJUGATE OF X(53) (0.5228, 0.0936) A B C X2167 X2148 X36 X54 X47 X48 X1 X1748 X336 X1930 X821 X1784 X921 X2168 X2169 (a, b, c) = (5, 6, 7) | AB = 1

X2169 (X2-ISOCONJUGATE OF X53) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X53
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(-5.474759260717\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos A \sec(B - C) : :\)

▸ Incident Central Lines6 lines

{1, 1748}, {36, 54}, {47, 48}, {336, 1930}, {821, 1784}, {921, 2168}

▸ Functional Relations4 relations

Notes

Let IaIbIc be the cevian triangle of I (incenter) and let A″ be the intersection of the perpendicular bisector of AIa and the line through Ia perpendicular line to BC; note that A″(lies on AX3). Define B″ and C″ cyclically. The finite fixed point of the affine transformation that carries ABC onto IaIbIc is X2197, and the finite fixed point of the affine transformation that carries IaIbIc onto A″B″C″ is X2269. (Angel Montesdeoca, December 7, 2021)