X2528

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

X2528 = X99-Ceva conjugate of X141
< 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, 647 }: Central Line L(39, 647) { 525, 669 }: Central Line L(525, 669) { 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_99 = STEINER POINT (0.1109, 0.4322) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) 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_2528 = RADICAL CENTER OF {ORTHOCENTROIDAL, BROCARD, (X(4),2R)} CIRCLES (-30.9919, 7.1543) A B C X99 X141 X39 X647 X525 X669 X826 X2474 X2528 (a, b, c) = (5, 6, 7) | AB = 1

X2528 (RADICAL CENTER OF {ORTHOCENTROIDAL, BROCARD, (X4,2R)} 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 \(f(a,b,c) = bc(b^{2} - c^{2})(b^{2} + c^{2})^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(82.373709037867\)

X2528 lies on the Kiepert parabola.

▸ Incident Central Lines3 lines

{39, 647}, {525, 669}, {826, 2474}

▸ Functional Relations3 relations