X2153

X2-ISOCONJUGATE OF X15

X2153 = trilinear product of circumcircle intercepts of inner Napoleon circle
< 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, 13 }: Central Line L(10, 13) { 1, 1094 }: Central Line L(1, 1094) { 37, 1250 }: Central Line L(37, 1250) { 31, 2154 }: Central Line L(31, 2154) { 65, 2306 }: Central Line L(65, 2306) { 2151, 2173 }: Central Line L(2151, 2173) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2173 = -ISOCONJUGATE OF X(74) (1.2293, 2.5968) X_2154 = -ISOCONJUGATE OF X(16) (0.9495, -0.1417) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_1 = INCENTER (0.5714, 0.2333) X_1094 = TRILINEAR SQUARE OF X(15) (0.5301, 0.1475) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1250 = ISOGONAL CONJUGATE OF X(1081) (0.5229, 0.1536) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_2306 = -ISOCONJUGATE OF X(1250) (0.6238, 0.3555) X_2151 = -ISOCONJUGATE OF X(13) (0.5852, 0.2196) X_2153 = -ISOCONJUGATE OF X(15) (0.6114, 0.3163) A B C X2173 X2154 X10 X13 X1 X1094 X37 X1250 X31 X65 X2306 X2151 X2153 (a, b, c) = (5, 6, 7) | AB = 1

X2153 (X2-ISOCONJUGATE OF X15) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X15
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(0.035392759147\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A \csc(A + \pi /3)\)

▸ Incident Central Lines6 lines

{1, 1094}, {10, 13}, {31, 2154}, {37, 1250}, {65, 2306}, {2151, 2173}

▸ Functional Relations2 relations