X2947

EXCENTRAL-ISOGONAL CONJUGATE OF X19

X2947 is the excentral-isogonal conjugate of X19.
< 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, 4 }: Incenter–Orthocenter Line { 71, 165 }: Central Line L(71, 165) { 43, 1754 }: Central Line L(43, 1754) { 971, 1214 }: Central Line L(971, 1214) { 846, 1709 }: Central Line L(846, 1709) { 152, 2822 }: Central Line L(152, 2822) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1754 = MIMOSA TRANSFORM OF X(284) (0.6792, 0.4313) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_1214 = ISOGONAL CONJUGATE OF X(1172) (0.5087, 0.1180) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_1709 = MIMOSA TRANSFORM OF X(9) (0.5826, 0.3739) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_2822 = ISOGONAL CONJUGATE OF X(2738) (0.6684, -0.3721) X_2947 = EXCENTRAL-ISOGONAL CONJUGATE OF X(19) (0.4145, -0.3913) A B C X219 X1 X4 X71 X165 X43 X1754 X971 X1214 X846 X1709 X152 X2822 X2947 (a, b, c) = (5, 6, 7) | AB = 1

X2947 (EXCENTRAL-ISOGONAL CONJUGATE OF X19) 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): \(-169.079821500065\)
▸ Incident Central Lines9 lines

{1, 4}, {9, 2954}, {40, 2939}, {43, 1754}, {71, 165}, {152, 2822}, {846, 1709}, {971, 1214}, {1282, 1763}

▸ Functional Relations4 relations