← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1518 ← Prev Overview · Code Next → X1518¶ ORTHOJOIN OF X8 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, 608 }: Central Line L(4, 608) 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_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_1518 = ORTHOJOIN OF X(8) (0.7658, 1.0514) A B C X4 X608 X1518 (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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1518 = ORTHOJOIN OF X(8) (0.6939, 0.9025) A B C X1518 (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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1518 = ORTHOJOIN OF X(8) (0.6685, 0.9576) A B C X1518 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, 608 }: Central Line L(4, 608) 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_608 = ISOGONAL CONJUGATE OF X(345) (0.6220, 0.2938) X_1518 = ORTHOJOIN OF X(8) (0.6380, 1.0647) A B C X4 X608 X1518 Kimberling (6, 9, 13) | AB = 1 X1518 (ORTHOJOIN OF X8) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 608} Related Centers: X4 (ORTHOCENTER), X608 (ISOGONAL CONJUGATE OF X345) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-8.147064273361\) ▸ Incident Central Lines1 line {4, 608}