X1470

X997-BETH CONJUGATE OF X997

X1470 = {X55,X56}-harmonic conjugate of X1319
< 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, 474 }: Central Line L(12, 474) { 108, 378 }: Central Line L(108, 378) { 388, 404 }: Central Line L(388, 404) { 6, 909 }: Central Line L(6, 909) { 11, 1012 }: Central Line L(11, 1012) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_997 = MIDPOINT OF X(1) AND X(200) (0.5053, 0.1685) 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_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_909 = POINT ADHAFERA (0.9286, -0.3499) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1012 = INTERCEPT OF EULER LINE AND LINE X(1)X(84) (0.5770, 0.3036) X_1470 = -BETH CONJUGATE OF X(997) (0.5950, 0.2766) A B C X997 X1 X3 X12 X474 X108 X378 X388 X404 X6 X909 X11 X1012 X1470 (a, b, c) = (5, 6, 7) | AB = 1

X1470 (X997-BETH CONJUGATE OF X997) 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 \(u : v : w\) = X997
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.602890743072\)
▸ Incident Central Lines12 lines

{1, 3}, {6, 909}, {11, 1012}, {12, 474}, {31, 1450}, {73, 1106}, {108, 378}, {109, 995}, {388, 404}, {603, 1193}, {1037, 1417}, {1407, 1464}

▸ Functional Relations1 relation