X2007

INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE)

X2007 is the insimilicenter(gallatly circle, incircle).
< 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, 39 }: Central Line L(1, 39) { 55, 1689 }: Central Line L(55, 1689) { 56, 1690 }: Central Line L(56, 1690) { 371, 1673 }: Central Line L(371, 1673) { 372, 1672 }: Central Line L(372, 1672) { 1124, 1670 }: Central Line L(1124, 1670) 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_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X(1342) (0.4118, -0.0436) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) A B C X1 X39 X55 X1689 X56 X1690 X371 X1673 X372 X1672 X1124 X1670 X2007 (a, b, c) = (5, 6, 7) | AB = 1

X2007 (INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1 + \sin(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.637407781623\)
▸ Incident Central Lines13 lines

{1, 39}, {11, 2009}, {12, 2010}, {55, 1689}, {56, 1690}, {57, 2017}, {181, 2019}, {371, 1673}, {372, 1672}, {1124, 1670}, {1335, 1671}, {1682, 2020}, {1697, 2018}