X3666

X42com(INTOUCH TRIANGLE)

X3666 = complement of X321
< 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) incircle: Incircle of △ABC { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 2, 37 }: Central Line L(2, 37) { 6, 63 }: Central Line L(6, 63) { 38, 42 }: Central Line L(38, 42) { 11, 114 }: Central Line L(11, 114) { 43, 210 }: Central Line L(43, 210) 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_2298 = -ISOCONJUGATE OF X(1193) (0.5765, 0.2431) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_3666 = com(INTOUCH TRIANGLE) (0.5661, 0.2236) A B C X1 X2298 X3 X2 X37 X6 X63 X38 X42 X11 X114 X43 X210 X3666 (a, b, c) = (5, 6, 7) | AB = 1

X3666 (X42com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(as + S_{A} : bs + S_{B} : cs + S_{C}\)
Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{2} + c^{2} + ab + ac)\)
Search Value (6, 9, 13): \(1.857741452646\)
▸ Incident Central Lines48 lines

{1, 3}, {2, 37}, {6, 63}, {7, 941}, {9, 2999}, {11, 114}, {21, 1104}, {27, 1841}, {31, 1386}, {38, 42}, {39, 712}, {43, 210}, {44, 3219}, {45, 3305}, {72, 386}, {77, 1407}, {81, 593}, {88, 1255}, {141, 306}, {191, 1203}, {226, 1465}, {227, 388}, {238, 846}, {239, 257}, {240, 1859}, {244, 1962}, {392, 995}, {474, 975}, {581, 1071}, {612, 1376}, {614, 968}, {650, 824}, {726, 1215}, {756, 899}, {896, 2308}, {918, 3310}, {960, 1193}, {1015, 2482}, {1036, 3556}, {1054, 1961}, {1150, 3187}, {1211, 2092}, {1279, 1621}, {1355, 1364}, {1396, 1870}, {1762, 2264}, {1817, 2303}, {2236, 2309}

▸ Functional Relations7 relations

Notes

Let A' be the trilinear pole of the tangent to the Apollonius circle where it meets the A-excircle, and define B' and C' cyclically. Triangle A'B'C' is homothetic to the medial triangle at X3666. (Randy Hutson, January 15, 2019)