X2488

RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD}

X2488 = reflection of X2495 in X2494
< 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) { 2495, 2494 }: Central Line L(2495, 2494) { 187, 237 }: Central Line L(187, 237) { 513, 676 }: Central Line L(513, 676) { 650, 926 }: Central Line L(650, 926) { 884, 2194 }: Central Line L(884, 2194) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2495 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 2nd LEMOINE CIRCLE} (-2.6701, 2.6976) X_2494 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 1st LEMOINE CIRCLE} (4.6935, -1.3106) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_926 = CROSSDIFFERENCE OF X(6) AND X(7) (0.0512, -0.1286) X_884 = ISOGONAL CONJUGATE OF X(883) (1.0241, 0.0337) X_2194 = -ISOCONJUGATE OF X(226) (0.5954, 0.2416) X_2488 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD} (12.0571, -5.3189) A B C X2495 X2494 X187 X237 X513 X676 X650 X926 X884 X2194 X2488 (a, b, c) = (5, 6, 7) | AB = 1

X2488 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD}) 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 \(f(a,b,c) = a(b + c - a)(b - c)[(b - c)^{2} - ab - ac]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-8.937927616958\)
▸ Incident Central Lines4 lines

{187, 237}, {513, 676}, {650, 926}, {884, 2194}

▸ Functional Relations3 relations