X2097

REFLECTION OF X6 IN X57

X2097 is the reflection of X6 in X57.
< 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) { 6, 57 }: Central Line L(6, 57) { 141, 329 }: Central Line L(141, 329) { 527, 599 }: Central Line L(527, 599) { 19, 1122 }: Central Line L(19, 1122) { 517, 990 }: Central Line L(517, 990) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) X_599 = ISOTOMIC CONJUGATE OF X(598) (0.4748, 0.1327) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1122 = 1st GRINBERG POINT (0.6289, 0.3227) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_990 = INTERSECTION OF LINES X(1)X(7) AND X(3)X(37) (0.6104, 0.3234) X_2097 = REFLECTION OF X(6) IN X(57) (0.6275, 0.3549) A B C X6 X57 X141 X329 X527 X599 X19 X1122 X517 X990 X2097 (a, b, c) = (5, 6, 7) | AB = 1

X2097 (REFLECTION OF X6 IN X57) 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 noted just above X2093
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.231997912030\)
▸ Incident Central Lines9 lines

{6, 57}, {19, 1122}, {141, 329}, {511, 2095}, {517, 990}, {518, 2093}, {524, 2094}, {527, 599}, {1503, 2096}

▸ Functional Relations1 relation