X3097

INTERSECTION OF LINES X1X_39 AND X43X_63

X3097 = reflection of X1699 in X262
< 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) { 1699, 262 }: Central Line L(1699, 262) { 1, 39 }: Central Line L(1, 39) { 43, 63 }: Central Line L(43, 63) { 10, 194 }: Central Line L(10, 194) { 165, 511 }: Central Line L(165, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_1 = INCENTER (0.5714, 0.2333) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_3097 = INTERSECTION OF LINES X(1)X(39) AND X(43)X(63) (0.5799, 0.2296) A B C X1699 X262 X1 X39 X43 X63 X10 X194 X165 X511 X3097 (a, b, c) = (5, 6, 7) | AB = 1

X3097 (INTERSECTION OF LINES X1X_39 AND X43X_63) 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 \(f(a,b,c) = a(a + 2b + 2c)(b^{2} + c^{2}) - b^{2}c^{2}\)
Search Value (6, 9, 13): \(1.522536692132\)
▸ Incident Central Lines10 lines

{1, 39}, {2, 726}, {10, 194}, {43, 63}, {76, 1698}, {165, 511}, {262, 1699}, {984, 1575}, {1670, 1700}, {1671, 1701}

▸ Functional Relations1 relation