X3767

X3053com[T(a², a² - c²)]

X3767 is the center of the inellipse that is the barycentric square of the orthic axis. The Brianchon point (perspector) of the inellipse is X393. (Randy Hutson, October 15, 2018)
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3926 }: Central Line L(2, 3926) { 5, 6 }: Nine-Point–Symmedian Line { 4, 32 }: Central Line L(4, 32) { 2, 39 }: Central Line L(2, 39) { 20, 187 }: Central Line L(20, 187) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_3926 = com[INVERSE(n(TANGENTIAL TRIANGLE))] (0.2953, 0.0167) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_3767 = com[T(a2, a2 - c2)] (0.6585, 0.2916) A B C Ma Mb Mc X2 X3926 X5 X6 X4 X32 X39 X20 X187 X3767 (a, b, c) = (5, 6, 7) | AB = 1

X3767 (X3053com[T(a², a² - c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{4} + (b^{2} - c^{2})^{2} : b^{4} + (c^{2} - a^{2})^{2} : c^{4} + (a^{2} - b^{2})^{2}\)
Search Value (6, 9, 13): \(1.116357969383\)
▸ Incident Central Lines40 lines

{2, 39}, {3, 230}, {4, 32}, {5, 6}, {20, 187}, {25, 2353}, {30, 3053}, {53, 1598}, {69, 626}, {148, 3552}, {172, 1478}, {193, 625}, {216, 3547}, {232, 3542}, {235, 2138}, {315, 385}, {382, 1384}, {388, 2242}, {393, 800}, {427, 1184}, {497, 2241}, {498, 2276}, {499, 2275}, {574, 631}, {609, 3585}, {637, 1504}, {638, 1505}, {946, 1572}, {1015, 3086}, {1204, 1562}, {1368, 1611}, {1479, 1914}, {1500, 3085}, {1506, 3090}, {1714, 2238}, {1834, 2271}, {1899, 2450}, {1976, 2909}, {2023, 3095}, {3054, 3526}

▸ Functional Relations4 relations