X1674

INSIMILICENTER(INCIRCLE, BROCARD CIRCLE)

X1674 is the insimilicenter(incircle, Brocard circle).
< 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, 182 }: Central Line L(1, 182) { 11, 1348 }: Central Line L(11, 1348) { 12, 1349 }: Central Line L(12, 1349) { 55, 1341 }: Central Line L(55, 1341) { 56, 1340 }: Central Line L(56, 1340) { 1124, 1668 }: Central Line L(1124, 1668) 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_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5517, 0.2023) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5617, 0.2039) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5420, 0.1715) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5226, 0.1394) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) A B C X1 X182 X11 X1348 X12 X1349 X55 X1341 X56 X1340 X1124 X1668 X1674 (a, b, c) = (5, 6, 7) | AB = 1

X1674 (INSIMILICENTER(INCIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(e + \cos(A - \omega ) : :\)
Search Value (6, 9, 13): \(2.475767605710\)
▸ Linear Combinations3 combinations
▸ Incident Central Lines17 lines

{1, 182}, {2, 1679}, {8, 1678}, {11, 1348}, {12, 1349}, {55, 1341}, {56, 1340}, {57, 1704}, {181, 1693}, {1015, 2033}, {1124, 1668}, {1335, 1669}, {1500, 2034}, {1682, 1694}, {1697, 1705}, {2007, 2012}, {2008, 2011}