X1466

X936-BETH CONJUGATE OF X936

X1466 = {X1,X57}-harmonic conjugate of X37566
< 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) { 7, 404 }: Central Line L(7, 404) { 12, 443 }: Central Line L(12, 443) { 222, 386 }: Central Line L(222, 386) { 6, 603 }: Central Line L(6, 603) { 226, 474 }: Central Line L(226, 474) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_443 = COMPLEMENT OF X(452) (0.5427, 0.2138) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_1466 = -BETH CONJUGATE OF X(936) (0.6002, 0.2861) A B C X936 X1 X3 X7 X404 X12 X443 X222 X386 X6 X603 X226 X474 X1466 (a, b, c) = (5, 6, 7) | AB = 1

X1466 (X936-BETH CONJUGATE OF X936) 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 \(u : v : w\) = X936
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.562779268063\)
▸ Incident Central Lines14 lines

{1, 3}, {6, 603}, {7, 404}, {12, 443}, {42, 1106}, {73, 1407}, {221, 1193}, {222, 386}, {226, 474}, {284, 1408}, {388, 1376}, {1012, 1210}, {1191, 1450}, {1448, 1465}

▸ Functional Relations2 relations