X613

INTERSECTION OF LINES X1X_6 AND X56X_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 { 55, 182 }: Central Line L(55, 182) { 56, 511 }: Central Line L(56, 511) { 141, 499 }: Central Line L(141, 499) { 240, 608 }: Central Line L(240, 608) { 394, 614 }: Central Line L(394, 614) 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_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_613 = INTERSECTION OF LINES X(1)X(6) AND X(56)X(511) (0.7698, 0.2310) A B C X1 X6 X55 X182 X56 X511 X141 X499 X240 X608 X394 X614 X613 (a, b, c) = (5, 6, 7) | AB = 1

X613 (INTERSECTION OF LINES X1X_6 AND X56X_511) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(W - \sin A : W - \sin B : W - \sin C\), where \(W = (a^{2} + b^{2} + c^{2})/(4 \operatorname{area})\)
Barycentrics: \(a(W - \sin A) : b(W - \sin B) : c(W - \sin C)\)
Search Value (6, 9, 13): \(1.896183052451\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines8 lines

{1, 6}, {55, 182}, {56, 511}, {141, 499}, {222, 982}, {240, 608}, {394, 614}, {496, 1069}