← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1561 ← Prev Overview · Code Next → X1561¶ ORTHOJOIN OF X511 X1561 = reflection of X1555 in X1514 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) { 1555, 1514 }: Central Line L(1555, 1514) { 4, 32 }: Central Line L(4, 32) { 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_1555 = ORTHOJOIN OF X(182) (0.8638, 1.6017) X_1514 = ORTHOJOIN OF X(3) (0.6818, 1.1255) X_4 = ORTHOCENTER (0.6122, 0.3958) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1561 = ORTHOJOIN OF X(511) (0.4997, 0.6493) A B C X1555 X1514 X4 X32 X30 X113 X1561 (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) { 1555, 1514 }: Central Line L(1555, 1514) { 4, 32 }: Central Line L(4, 32) { 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_1555 = ORTHOJOIN OF X(182) (0.7045, 1.1812) X_1514 = ORTHOJOIN OF X(3) (0.6400, 0.9600) X_4 = ORTHOCENTER (0.6400, 0.4800) X_32 = 3rd POWER POINT (0.6819, 0.3119) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1561 = ORTHOJOIN OF X(511) (0.5755, 0.7388) A B C X1555 X1514 X4 X32 X30 X113 X1561 (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) { 1555, 1514 }: Central Line L(1555, 1514) { 4, 32 }: Central Line L(4, 32) { 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_1555 = ORTHOJOIN OF X(182) (0.6738, 1.2011) X_1514 = ORTHOJOIN OF X(3) (0.6180, 0.9717) X_4 = ORTHOCENTER (0.6180, 0.4859) X_32 = 3rd POWER POINT (0.6545, 0.3180) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1561 = ORTHOJOIN OF X(511) (0.5623, 0.7423) A B C X1555 X1514 X4 X32 X30 X113 X1561 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) { 1555, 1514 }: Central Line L(1555, 1514) { 4, 32 }: Central Line L(4, 32) { 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_1555 = ORTHOJOIN OF X(182) (0.6298, 1.0979) X_1514 = ORTHOJOIN OF X(3) (0.6249, 1.0565) X_4 = ORTHOCENTER (0.6331, 0.8294) X_32 = 3rd POWER POINT (0.6767, 0.2196) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1561 = ORTHOJOIN OF X(511) (0.6199, 1.0152) A B C X1555 X1514 X4 X32 X30 X113 X1561 Kimberling (6, 9, 13) | AB = 1 X1561 (ORTHOJOIN OF X511) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {1555, 1514} Related Centers: X1555 (ORTHOJOIN OF X182), X1514 (ORTHOJOIN OF X3) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-7.491371149843\) ▸ Incident Central Lines2 lines {4, 32}, {30, 113} ▸ Functional Relations2 relations X1561 = reflection of X1555 in X1514 X1561 = orthopole of PU(45)
