X3723

X1213com(INCENTRAL TRIANGLE)

X3723 = complement of X5564
< 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 { 86, 536 }: Central Line L(86, 536) { 594, 1125 }: Central Line L(594, 1125) { 519, 1213 }: Central Line L(519, 1213) { 583, 1334 }: Central Line L(583, 1334) { 941, 1392 }: Central Line L(941, 1392) 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_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_1334 = POINT ALYA (0.5324, 0.1760) X_941 = ISOGONAL CONJUGATE OF X(940) (0.5671, 0.2256) X_1392 = ISOGONAL CONJUGATE OF X(1388) (0.6149, 0.4463) X_3723 = com(INCENTRAL TRIANGLE) (0.5678, 0.2290) A B C X1 X6 X86 X536 X594 X1125 X519 X1213 X583 X1334 X941 X1392 X3723 (a, b, c) = (5, 6, 7) | AB = 1

X3723 (X1213com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(2a + 3b + 3c)\)
Search Value (6, 9, 13): \(1.786850815418\)
▸ Linear Combinations1 combination

  • X3723 = X86com[n(Medial)*n(Incentral)]

▸ Incident Central Lines17 lines

{1, 6}, {86, 536}, {519, 1213}, {551, 2321}, {583, 1334}, {594, 1125}, {902, 1962}, {910, 1953}, {941, 1392}, {966, 3241}, {1055, 2294}, {1319, 2171}, {1388, 2285}, {2178, 3295}, {2280, 3204}, {2345, 3622}, {2667, 3009}

▸ Functional Relations2 relations