X1497

POINT BETELGEUSE II

X1497 = {X1,X31}-harmonic conjugate of X255
< 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, 31 }: Central Line L(1, 31) { 1, 21 }: Central Line L(1, 21) { 82, 158 }: Central Line L(82, 158) { 55, 602 }: Central Line L(55, 602) { 56, 601 }: Central Line L(56, 601) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_1 = INCENTER (0.5714, 0.2333) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_1497 = POINT BETELGEUSE II (0.5934, 0.2621) A B C X255 X1 X31 X21 X82 X158 X55 X602 X56 X601 X1497 (a, b, c) = (5, 6, 7) | AB = 1

X1497 (POINT BETELGEUSE II) 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 \(f(A,B,C) = 1 + \sin^{2} A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.302531797960\)
▸ Incident Central Lines12 lines

{1, 21}, {3, 1057}, {46, 1471}, {55, 602}, {56, 601}, {82, 158}, {498, 748}, {499, 750}, {517, 1451}, {603, 999}, {605, 1335}, {606, 1124}

▸ Functional Relations1 relation