← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1524 ← Prev Overview · Code Next → X1524¶ ORTHOJOIN OF X15 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, 13 }: Central Line L(4, 13) { 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1524 = ORTHOJOIN OF X(15) (0.8784, 1.6400) A B C X4 X13 X30 X113 X1524 (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, 13 }: Central Line L(4, 13) { 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6188, 0.2763) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1524 = ORTHOJOIN OF X(15) (0.7176, 1.2260) A B C X4 X13 X30 X113 X1524 (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, 13 }: Central Line L(4, 13) { 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6001, 0.2799) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1524 = ORTHOJOIN OF X(15) (0.6843, 1.2443) A B C X4 X13 X30 X113 X1524 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, 13 }: Central Line L(4, 13) { 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6324, 0.2733) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1524 = ORTHOJOIN OF X(15) (0.6336, 1.1287) A B C X4 X13 X30 X113 X1524 Kimberling (6, 9, 13) | AB = 1 X1524 (ORTHOJOIN OF X15) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 13}, {30, 113} Related Centers: X4 (ORTHOCENTER), X13 (1st ISOGONIC CENTER), 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): \(-8.772700320179\) ▸ Incident Central Lines2 lines {4, 13}, {30, 113} ▸ Functional Relations1 relation X1524 = reflection of Xi in Xj for these (i,j): (1525, 1514), (1546, 1525)
