X2514

RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X4,2R)}

The circle (X4,2R) is identified at X2474.
< 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) { 669, 2485 }: Central Line L(669, 2485) { 325, 523 }: Central Line L(325, 523) { 512, 1692 }: Central Line L(512, 1692) { 525, 2474 }: Central Line L(525, 2474) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (2.1894, 0.2056) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7995, 0.5968) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (6.9649, -4.0371) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (8.7303, -4.2052) A B C X669 X2485 X325 X523 X512 X1692 X525 X2474 X2514 (a, b, c) = (5, 6, 7) | AB = 1

X2514 (RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X4,2R)}) 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 \(f(a,b,c) = a(b^{2} - c^{2})[b^{4} + c^{4} + a^{2}b^{2} + a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-7.319817647333\)
▸ Incident Central Lines4 lines

{325, 523}, {512, 1692}, {525, 2474}, {669, 2485}

▸ Functional Relations3 relations