X3076

INTERSECTION OF X1X_606 AND X47X_605

< 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, 372 }: Central Line L(212, 372) { 1, 606 }: Central Line L(1, 606) { 47, 605 }: Central Line L(47, 605) { 371, 603 }: Central Line L(371, 603) { 31, 1125 }: Central Line L(31, 1125) 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_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_1 = INCENTER (0.5714, 0.2333) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_3076 = INTERSECTION OF X(1)X(606) AND X(47)X(605) (0.5590, 0.2142) A B C X6 X255 X212 X372 X1 X606 X47 X605 X371 X603 X31 X1125 X3076 (a, b, c) = (5, 6, 7) | AB = 1

X3076 (INTERSECTION OF X1X_606 AND X47X_605) 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): \(1.779658086114\)
▸ Incident Central Lines12 lines

{1, 606}, {6, 255}, {31, 1125}, {47, 605}, {109, 1702}, {212, 372}, {371, 603}, {601, 2066}, {1587, 1936}, {1588, 1935}, {3068, 3075}, {3069, 3074}