X1454

X498-BETH CONJUGATE OF X498

< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 12, 63 }: Central Line L(12, 63) { 90, 381 }: Central Line L(90, 381) { 208, 407 }: Central Line L(208, 407) { 5, 920 }: Central Line L(5, 920) { 201, 750 }: Central Line L(201, 750) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_407 = CROSSPOINT OF X(4) AND X(225) (0.6211, 0.4189) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_1454 = -BETH CONJUGATE OF X(498) (0.6215, 0.3253) A B C X498 X1 X3 X12 X63 X90 X381 X208 X407 X5 X920 X201 X750 X1454 (a, b, c) = (5, 6, 7) | AB = 1

X1454 (X498-BETH CONJUGATE OF X498) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X498
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.253521192637\)
▸ Incident Central Lines11 lines

{1, 3}, {5, 920}, {12, 63}, {31, 1393}, {34, 1399}, {90, 381}, {201, 750}, {208, 407}, {453, 1014}, {603, 1254}, {1406, 1427}