X3077

INTERSECTION OF X1X_605 AND X47X_606

< 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) { 6, 255 }: Central Line L(6, 255) { 212, 371 }: Central Line L(212, 371) { 1, 605 }: Central Line L(1, 605) { 47, 606 }: Central Line L(47, 606) { 372, 603 }: Central Line L(372, 603) { 31, 1135 }: Central Line L(31, 1135) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1 = INCENTER (0.5714, 0.2333) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1135 = 4th MORLEY-TAYLOR-MARR CENTER (0.5834, 0.2515) X_3077 = INTERSECTION OF X(1)X(605) AND X(47)X(606) (0.6759, 0.3655) A B C X6 X255 X212 X371 X1 X605 X47 X606 X372 X603 X31 X1135 X3077 (a, b, c) = (5, 6, 7) | AB = 1

X3077 (INTERSECTION OF X1X_605 AND X47X_606) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos^{2} A - \sin A : \cos^{2} B - \sin B : \cos^{2} C - \sin C\)
Barycentrics: \((\sin A)(\cos^{2} A - \sin A) : (\sin B)(\cos^{2} B - \sin B) : (\sin C)(\cos^{2} C - \sin C)\)
Search Value (6, 9, 13): \(-3.673556898997\)
▸ Incident Central Lines12 lines

{1, 605}, {6, 255}, {31, 1135}, {47, 606}, {109, 1703}, {212, 371}, {372, 603}, {602, 2067}, {1587, 1935}, {1588, 1936}, {3068, 3074}, {3069, 3075}