X3029

INTERSECTION X10X_115∩X98X_573

X3029 = complement of X38481
< 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) { 10, 115 }: Central Line L(10, 115) { 99, 386 }: Central Line L(99, 386) { 98, 573 }: Central Line L(98, 573) { 114, 2051 }: Central Line L(114, 2051) { 181, 3027 }: Central Line L(181, 3027) { 690, 2782 }: Central Line L(690, 2782) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_99 = STEINER POINT (0.1109, 0.4322) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_98 = TARRY POINT (0.8891, -0.2281) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_2051 = EXSIMILICENTER(NINE-POINT CIRCLE, APOLLONIUS CIRCLE) (0.6034, 0.3358) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_3027 = INCIRCLE-ANTIPODE OF X(3023) (0.3936, 0.3842) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0840, -0.1726) X_2782 = ISOGONAL CONJUGATE OF X(2698) (0.9849, -0.1797) X_3029 = INTERSECTION X(10)X(115)∩X(98)X(573) (-1.1309, 0.8967) A B C X10 X115 X99 X386 X98 X573 X114 X2051 X181 X3027 X690 X2782 X3029 (a, b, c) = (5, 6, 7) | AB = 1

X3029 (INTERSECTION X10X_115∩X98X_573) 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 \(f(a,b,c) = bc(b + c)^{2}(a^{3} + a^{2}c - ab^{2} - b^{3})(a^{3} + a^{2}b - ac^{2} - c^{3})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.032807635754\)

X3029 lies on the Apollonius circle.

▸ Incident Central Lines12 lines

{10, 115}, {98, 573}, {99, 386}, {114, 2051}, {181, 3027}, {690, 2782}, {970, 2782}, {1682, 3023}, {2786, 3033}, {2787, 3032}, {2795, 3034}, {2796, 3030}

▸ Functional Relations1 relation

  • X3029 = complement of X38481