← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1545 ← Prev Overview · Code Next → X1545¶ ORTHOJOIN OF X61 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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1545 = ORTHOJOIN OF X(61) (1.2717, 2.6689) A B C X4 X15 X30 X113 X1545 (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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5764, 0.1310) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1545 = ORTHOJOIN OF X(61) (0.8728, 1.7581) A B C X4 X15 X30 X113 X1545 (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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5641, 0.1319) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1545 = ORTHOJOIN OF X(61) (0.8167, 1.7895) A B C X4 X15 X30 X113 X1545 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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.6000, 0.0051) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1545 = ORTHOJOIN OF X(61) (0.6510, 1.2730) A B C X4 X15 X30 X113 X1545 Kimberling (6, 9, 13) | AB = 1 X1545 (ORTHOJOIN OF X61) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 15}, {30, 113} Related Centers: X4 (ORTHOCENTER), X15 (1st 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): \(-10.401588665114\) ▸ Incident Central Lines2 lines {4, 15}, {30, 113} ▸ Functional Relations1 relation X1545 = reflection of Xi in Xj for these (i,j): (1525, 1524), (1546, 1514)
