← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1546 ← Prev Overview · Code Next → X1546¶ ORTHOJOIN OF X62 5, 6, 7 3, 4, 5 Kepler Kimberling < 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) { 4, 16 }: Central Line L(4, 16) { 30, 113 }: Central Line L(30, 113) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1546 = ORTHOJOIN OF X(62) (0.0919, -0.4180) A B C X4 X16 X30 X113 X1546 (a, b, c) = (5, 6, 7) | AB = 1 < 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) { 4, 16 }: Central Line L(4, 16) { 30, 113 }: Central Line L(30, 113) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_4 = ORTHOCENTER (0.6400, 0.4800) X_16 = 2nd ISODYNAMIC POINT (1.3303, 1.4234) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1546 = ORTHOJOIN OF X(62) (0.4072, 0.1619) A B C X4 X16 X30 X113 X1546 (a, b, c) = (3, 4, 5) | AB = 1 < 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) { 4, 16 }: Central Line L(4, 16) { 30, 113 }: Central Line L(30, 113) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_4 = ORTHOCENTER (0.6180, 0.4859) X_16 = 2nd ISODYNAMIC POINT (1.2449, 1.5332) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1546 = ORTHOJOIN OF X(62) (0.4194, 0.1540) A B C X4 X16 X30 X113 X1546 Kepler (1, √φ, φ) | AB = 1 < 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) { 4, 16 }: Central Line L(4, 16) { 30, 113 }: Central Line L(30, 113) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_4 = ORTHOCENTER (0.6331, 0.8294) X_16 = 2nd ISODYNAMIC POINT (0.8687, 0.7568) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1546 = ORTHOJOIN OF X(62) (0.5987, 0.8400) A B C X4 X16 X30 X113 X1546 Kimberling (6, 9, 13) | AB = 1 X1546 (ORTHOJOIN OF X62) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 16}, {30, 113} Related Centers: X4 (ORTHOCENTER), X16 (2nd ISODYNAMIC POINT), X30 (EULER INFINITY POINT), X113 (JERABEK ANTIPODE) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-5.514923630308\) ▸ Incident Central Lines2 lines {4, 16}, {30, 113} ▸ Functional Relations1 relation X1546 = reflection of Xi in Xj for these (i,j): (1524, 1525), (1545, 1514)
