← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1517 ← Prev Overview · Code Next → X1517¶ ORTHOJOIN OF X7 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, 218 }: Central Line L(4, 218) 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_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_1517 = ORTHOJOIN OF X(7) (4.9304, -5.8111) A B C X4 X218 X1517 (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, 218 }: Central Line L(4, 218) 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_218 = -CEVA CONJUGATE OF X(55) (0.7158, 0.3158) X_1517 = ORTHOJOIN OF X(7) (1.6625, -1.7354) A B C X4 X218 X1517 (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, 218 }: Central Line L(4, 218) 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_218 = -CEVA CONJUGATE OF X(55) (0.6829, 0.3209) X_1517 = ORTHOJOIN OF X(7) (1.5111, -1.7862) A B C X4 X218 X1517 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, 218 }: Central Line L(4, 218) 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_218 = -CEVA CONJUGATE OF X(55) (0.7347, 0.2309) X_1517 = ORTHOJOIN OF X(7) (0.6818, 0.5426) A B C X4 X218 X1517 Kimberling (6, 9, 13) | AB = 1 X1517 (ORTHOJOIN OF X7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 218} Related Centers: X4 (ORTHOCENTER), X218 (-CEVA CONJUGATE OF X55) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-3.097255701358\) ▸ Incident Central Lines1 line {4, 218}