X3721

X213com(INCENTRAL TRIANGLE)

X3721 = crosspoint of X1 and X76
< 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, 32 }: Central Line L(1, 32) { 37, 65 }: Central Line L(37, 65) { 257, 335 }: Central Line L(257, 335) { 10, 762 }: Central Line L(10, 762) { 213, 758 }: Central Line L(213, 758) { 6, 977 }: Central Line L(6, 977) 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_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_762 = TRILINEAR CUBE OF X(37) (0.5240, 0.1822) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_977 = ISOGONAL CONJUGATE OF X(976) (0.5890, 0.2525) X_3721 = com(INCENTRAL TRIANGLE) (0.5343, 0.1792) A B C X1 X76 X32 X37 X65 X257 X335 X10 X762 X213 X758 X6 X977 X3721 (a, b, c) = (5, 6, 7) | AB = 1

X3721 (X213com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{3} + c^{3} : :\)
Barycentrics: \(a(b + c)(b^{2} + c^{2} - bc)\)
Search Value (6, 9, 13): \(2.685976871927\)
▸ Incident Central Lines19 lines

{1, 32}, {6, 977}, {10, 762}, {37, 65}, {38, 1107}, {42, 2240}, {72, 2238}, {76, 1928}, {213, 758}, {257, 335}, {321, 1237}, {350, 695}, {712, 1930}, {737, 789}, {960, 3290}, {982, 2275}, {986, 2276}, {1574, 1739}, {1964, 2237}

▸ Functional Relations3 relations