X611

INTERSECTION OF LINES X1X_6 AND X55X_511

< 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, 6 }: Incenter–Symmedian Line { 56, 182 }: Central Line L(56, 182) { 55, 511 }: Central Line L(55, 511) { 141, 498 }: Central Line L(141, 498) { 240, 607 }: Central Line L(240, 607) { 394, 612 }: Central Line L(394, 612) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_611 = INTERSECTION OF LINES X(1)X(6) AND X(55)X(511) (0.5730, 0.2352) A B C X1 X6 X56 X182 X55 X511 X141 X498 X240 X607 X394 X612 X611 (a, b, c) = (5, 6, 7) | AB = 1

X611 (INTERSECTION OF LINES X1X_6 AND X55X_511) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(D + \sin A : D + \sin B : D + \sin C\), where \(D = (a^{2} + b^{2} + c^{2})/(4 \operatorname{area})\)
Barycentrics: \(a(D + \sin A) : b(D + \sin B) : c(D + \sin C)\)
Search Value (6, 9, 13): \(1.560860710962\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(S^{2} + bc S_{\omega}) : :\)

▸ Incident Central Lines6 lines

{1, 6}, {55, 511}, {56, 182}, {141, 498}, {240, 607}, {394, 612}