← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1516 ← Prev Overview · Code Next → X1516¶ ORTHOJOIN OF X5 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, 96 }: Central Line L(4, 96) { 187, 1514 }: Central Line L(187, 1514) 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_96 = ISOGONAL CONJUGATE OF X(52) (-0.0943, -0.0197) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_1514 = ORTHOJOIN OF X(3) (0.6818, 1.1255) X_1516 = ORTHOJOIN OF X(5) (2.7335, 1.6430) A B C X4 X96 X187 X1514 X1516 (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, 96 }: Central Line L(4, 96) { 187, 1514 }: Central Line L(187, 1514) 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_96 = ISOGONAL CONJUGATE OF X(52) (1.7371, 0.1600) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.9534, 0.7772) X_1514 = ORTHOJOIN OF X(3) (0.6400, 0.9600) X_1516 = ORTHOJOIN OF X(5) (2.2857, 0.0000) A B C X4 X96 X187 X1514 X1516 (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, 96 }: Central Line L(4, 96) { 187, 1514 }: Central Line L(187, 1514) 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_96 = ISOGONAL CONJUGATE OF X(52) (1.9514, 0.1620) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.9045, 0.8325) X_1514 = ORTHOJOIN OF X(3) (0.6180, 0.9717) X_1516 = ORTHOJOIN OF X(5) (2.6180, 0.0000) A B C X4 X96 X187 X1514 X1516 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, 96 }: Central Line L(4, 96) { 187, 1514 }: Central Line L(187, 1514) 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_96 = ISOGONAL CONJUGATE OF X(52) (1.1396, 0.0192) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.7344, 0.3809) X_1514 = ORTHOJOIN OF X(3) (0.6249, 1.0565) X_1516 = ORTHOJOIN OF X(5) (0.6717, 0.7678) A B C X4 X96 X187 X1514 X1516 Kimberling (6, 9, 13) | AB = 1 X1516 (ORTHOJOIN OF X5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 96}, {187, 1514} Related Centers: X4 (ORTHOCENTER), X96 (ISOGONAL CONJUGATE OF X52), X187 (INVERSE-IN-CIRCUMCIRCLE OF X), 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): \(-5.343718804898\) ▸ Incident Central Lines2 lines {4, 96}, {187, 1514}
