X3622

H(X8; M,-1/2)

X3622 = {X1,X2}-harmonic conjugate of X145
< 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, 2 }: Nagel Line { 149, 377 }: Central Line L(149, 377) { 21, 999 }: Central Line L(21, 999) { 144, 1001 }: Central Line L(144, 1001) { 81, 1191 }: Central Line L(81, 1191) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_1191 = 2nd SARAGOSSA POINT OF X(56) (0.6211, 0.2922) X_3622 = H(X(8); M,-1/2) (0.5569, 0.2190) A B C X145 X1 X2 X149 X377 X21 X999 X144 X1001 X81 X1191 X3622 (a, b, c) = (5, 6, 7) | AB = 1

X3622 (H(X8; M,-1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 r + R \sin B \sin C : :\)
Barycentrics: \(5a + b + c : 5b + c + a : 5c + a + b\)
Search Value (6, 9, 13): \(2.092762916471\)
▸ Linear Combinations1 combination
▸ Incident Central Lines34 lines

{1, 2}, {7, 1420}, {20, 1385}, {21, 999}, {56, 1621}, {79, 2320}, {81, 1191}, {86, 3445}, {100, 3303}, {144, 1001}, {149, 377}, {193, 1386}, {320, 1279}, {388, 1388}, {390, 2646}, {391, 1100}, {404, 3295}, {452, 3487}, {4496, 2476}, {497, 2475}, {517, 3523}, {631, 1482}, {940, 1616}, {944, 3091}, {946, 3146}, {952, 3090}, {962, 3522}, {1056, 2478}, {1219, 1255}, {1319, 3485}, {1483, 1656}, {1697, 3306}, {2325, 3247}, {3218, 3333}

▸ Functional Relations1 relation