X740

EVEN (- 1, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X740 lies on the line at infinity.
< 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, 37 }: Central Line L(10, 37) { 1, 75 }: Central Line L(1, 75) { 8, 192 }: Central Line L(8, 192) { 43, 312 }: Central Line L(43, 312) { 42, 321 }: Central Line L(42, 321) { 238, 239 }: Central Line L(238, 239) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_8 = NAGEL POINT (0.4694, 0.1333) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) A B C X741 X10 X37 X1 X75 X8 X192 X43 X312 X42 X321 X238 X239 X740 (a, b, c) = (5, 6, 7) | AB = 1

X740 (EVEN (- 1, 1) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a ^{-2}(b^{1} + c^{1}) - a^{0}(b ^{-1} + c ^{-1}) : :\)
Barycentrics: \((a^{2} - b c) (b + c) : :\)
▸ Incident Central Lines8 lines

{1, 75}, {8, 192}, {10, 37}, {30, 511}, {42, 321}, {43, 312}, {238, 239}, {872, 1089}

▸ Functional Relations9 relations

Notes

Let A'B'C' be the outer Garcia triangle and A″B″C″ the inner Garcia triangle. X740 is the radical center of the circumcircles of AA'A″, BB'B″, CC'C″. (Randy Hutson, January 29, 2018)