X2451

INVERSE-IN-2nd-LEMOINE-CIRCLE OF X1316

X2451 = inverse-in-2nd-Lemoine-circle of X1316
< 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, 523 }: Central Line L(6, 523) { 647, 657 }: Central Line L(647, 657) { 512, 1570 }: Central Line L(512, 1570) { 520, 2489 }: Central Line L(520, 2489) 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_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_657 = CROSSDIFFERENCE OF X(1) AND X(7) (10.1538, -2.2611) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.4005, -0.0623) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.1726, 0.9764) X_2451 = INVERSE-IN-2nd-LEMOINE-CIRCLE OF X(1316) (-1.4168, 1.0380) A B C X6 X648 X523 X647 X657 X512 X1570 X520 X2489 X2451 (a, b, c) = (5, 6, 7) | AB = 1

X2451 (INVERSE-IN-2nd-LEMOINE-CIRCLE OF X1316) 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 \(f(a,b,c) = a(b^{2} - c^{2})(a^{4} + 2b^{2}c^{2} - a^{2}b^{2}- a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.263906722126\)
▸ Incident Central Lines4 lines

{6, 523}, {512, 1570}, {520, 2489}, {647, 657}

▸ Functional Relations6 relations