X1496

POINT BETELGEUSE I

X1496 = {X1,X63}-harmonic conjugate of X774
< 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, 63 }: Central Line L(1, 63) { 1, 21 }: Central Line L(1, 21) { 56, 212 }: Central Line L(56, 212) { 55, 603 }: Central Line L(55, 603) { 75, 775 }: Central Line L(75, 775) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_1 = INCENTER (0.5714, 0.2333) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_775 = ISOGONAL CONJUGATE OF X(774) (0.4699, 0.1510) X_1496 = POINT BETELGEUSE I (0.5410, 0.1932) A B C X774 X1 X63 X21 X56 X212 X55 X603 X75 X775 X1496 (a, b, c) = (5, 6, 7) | AB = 1

X1496 (POINT BETELGEUSE I) 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 \(f(A,B,C) = 1 + \cos^{2} A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.083322135282\)
▸ Incident Central Lines9 lines

{1, 21}, {3, 1037}, {48, 820}, {55, 603}, {56, 212}, {75, 775}, {354, 1451}, {580, 1471}, {602, 999}

▸ Functional Relations1 relation