X2531

RADICAL CENTER OF {BROCARD, (X4,2R), 2nd BROCARD} CIRCLES

X2531 = bicentric difference of PU(156)
< 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) { 39, 512 }: Central Line L(39, 512) { 99, 783 }: Central Line L(99, 783) { 525, 2513 }: Central Line L(525, 2513) { 826, 2474 }: Central Line L(826, 2474) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_99 = STEINER POINT (0.1109, 0.4322) X_783 = o-(- 4, 4) CIRCUMCIRCLE POINT (0.9757, -0.0828) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2513 = RADICAL CENTER OF {CIRCUMCIRCLE, GALLATLY CIRCLE, (X(4),2R)} (9.6264, -4.5477) X_826 = ODD (0, 4) INFINITY POINT (1.1003, 0.0340) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (6.9649, -4.0371) X_2531 = RADICAL CENTER OF {BROCARD, (X(4),2R), 2nd BROCARD} CIRCLES (8.2533, -4.4169) A B C X39 X512 X99 X783 X525 X2513 X826 X2474 X2531 (a, b, c) = (5, 6, 7) | AB = 1

X2531 (RADICAL CENTER OF {BROCARD, (X4,2R), 2nd BROCARD} CIRCLES) 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 \(f(a,b,c) = a^{3}(b^{2} - c^{2})(b^{2} + c^{2})^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-4.705201944249\)
▸ Incident Central Lines4 lines

{39, 512}, {99, 783}, {525, 2513}, {826, 2474}

▸ Functional Relations1 relation

  • X2531 = bicentric difference of PU(156)