← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1555 ← Prev Overview · Code Next → X1555¶ ORTHOJOIN OF X182 X1555 = reflection of X1561 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) { 1561, 1514 }: Central Line L(1561, 1514) { 4, 39 }: Central Line L(4, 39) { 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_1561 = ORTHOJOIN OF X(511) (0.4997, 0.6493) X_1514 = ORTHOJOIN OF X(3) (0.6818, 1.1255) X_4 = ORTHOCENTER (0.6122, 0.3958) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1555 = ORTHOJOIN OF X(182) (0.8638, 1.6017) A B C X1561 X1514 X4 X39 X30 X113 X1555 (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) { 1561, 1514 }: Central Line L(1561, 1514) { 4, 39 }: Central Line L(4, 39) { 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_1561 = ORTHOJOIN OF X(511) (0.5755, 0.7388) X_1514 = ORTHOJOIN OF X(3) (0.6400, 0.9600) X_4 = ORTHOCENTER (0.6400, 0.4800) X_39 = BROCARD MIDPOINT (0.6138, 0.1951) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1555 = ORTHOJOIN OF X(182) (0.7045, 1.1812) A B C X1561 X1514 X4 X39 X30 X113 X1555 (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) { 1561, 1514 }: Central Line L(1561, 1514) { 4, 39 }: Central Line L(4, 39) { 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_1561 = ORTHOJOIN OF X(511) (0.5623, 0.7423) X_1514 = ORTHOJOIN OF X(3) (0.6180, 0.9717) X_4 = ORTHOCENTER (0.6180, 0.4859) X_39 = BROCARD MIDPOINT (0.5955, 0.1965) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1555 = ORTHOJOIN OF X(182) (0.6738, 1.2011) A B C X1561 X1514 X4 X39 X30 X113 X1555 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) { 1561, 1514 }: Central Line L(1561, 1514) { 4, 39 }: Central Line L(4, 39) { 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_1561 = ORTHOJOIN OF X(511) (0.6199, 1.0152) X_1514 = ORTHOJOIN OF X(3) (0.6249, 1.0565) X_4 = ORTHOCENTER (0.6331, 0.8294) X_39 = BROCARD MIDPOINT (0.6418, 0.1220) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1555 = ORTHOJOIN OF X(182) (0.6298, 1.0979) A B C X1561 X1514 X4 X39 X30 X113 X1555 Kimberling (6, 9, 13) | AB = 1 X1555 (ORTHOJOIN OF X182) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {1561, 1514} Related Centers: X1561 (ORTHOJOIN OF X511), 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): \(-8.425141145580\) ▸ Incident Central Lines2 lines {4, 39}, {30, 113} ▸ Functional Relations1 relation X1555 = reflection of X1561 in X1514
