← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1534 ← Prev Overview · Code Next → X1534¶ ORTHOJOIN OF X40 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, 937 }: Central Line L(4, 937) 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_937 = ISOGONAL CONJUGATE OF X(936) (0.6143, 0.2920) X_1534 = ORTHOJOIN OF X(40) (0.6016, 0.9221) A B C X4 X937 X1534 (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, 937 }: Central Line L(4, 937) 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_937 = ISOGONAL CONJUGATE OF X(936) (0.6553, 0.2681) X_1534 = ORTHOJOIN OF X(40) (0.6123, 0.8631) A B C X4 X937 X1534 (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, 937 }: Central Line L(4, 937) 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_937 = ISOGONAL CONJUGATE OF X(936) (0.6313, 0.2721) X_1534 = ORTHOJOIN OF X(40) (0.5942, 0.8702) A B C X4 X937 X1534 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, 937 }: Central Line L(4, 937) 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_937 = ISOGONAL CONJUGATE OF X(936) (0.6644, 0.1873) X_1534 = ORTHOJOIN OF X(40) (0.6231, 1.0364) A B C X4 X937 X1534 Kimberling (6, 9, 13) | AB = 1 X1534 (ORTHOJOIN OF X40) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 937} Related Centers: X4 (ORTHOCENTER), X937 (ISOGONAL CONJUGATE OF X936) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-7.736206603991\) ▸ Incident Central Lines1 line {4, 937}