X1703

EXSIMILICENTER(BEVAN CIRCLE, 2nd LEMOINE CIRCLE)

X1703 is the exsimilicenter(Bevan circle, 2nd Lemoine 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) { 6, 40 }: Central Line L(6, 40) { 1, 372 }: Central Line L(1, 372) { 165, 371 }: Central Line L(165, 371) { 580, 606 }: Central Line L(580, 606) { 9, 1377 }: Central Line L(9, 1377) { 57, 1335 }: Central Line L(57, 1335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_40 = BEVAN POINT (0.4286, -0.0292) X_1 = INCENTER (0.5714, 0.2333) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5443, 0.2084) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_1703 = EXSIMILICENTER(BEVAN CIRCLE, 2nd LEMOINE CIRCLE) (0.6625, 0.3753) A B C X6 X40 X1 X372 X165 X371 X580 X606 X9 X1377 X57 X1335 X1703 (a, b, c) = (5, 6, 7) | AB = 1

X1703 (EXSIMILICENTER(BEVAN CIRCLE, 2nd LEMOINE CIRCLE)) 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 \(f(A,B,C) = 2 \sin A - \cos A + \cos B + \cos C - 1\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.164899585731\)
▸ Incident Central Lines22 lines

{1, 372}, {6, 40}, {9, 1377}, {10, 1587}, {43, 1686}, {57, 1335}, {165, 371}, {485, 1698}, {486, 1699}, {516, 1588}, {580, 606}, {1124, 1697}, {1378, 1706}, {1504, 1571}, {1505, 1572}, {1668, 1705}, {1669, 1704}, {1670, 2018}, {1671, 2017}, {1685, 1695}, {1687, 1700}, {1688, 1701}