← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1520 ← Prev Overview · Code Next → X1520¶ ORTHOJOIN OF X10 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, 572 }: Central Line L(4, 572) 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_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_1520 = ORTHOJOIN OF X(10) (0.9445, 1.3587) A B C X4 X572 X1520 (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, 572 }: Central Line L(4, 572) 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_572 = ORTHOGONAL OF X(58) (0.2356, 0.0000) X_1520 = ORTHOJOIN OF X(10) (0.7882, 1.0765) A B C X4 X572 X1520 (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, 572 }: Central Line L(4, 572) 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_572 = ORTHOGONAL OF X(58) (0.6858, 0.0000) X_1520 = ORTHOJOIN OF X(10) (0.7545, 1.1447) A B C X4 X572 X1520 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, 572 }: Central Line L(4, 572) 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_572 = ORTHOGONAL OF X(58) (1.1910, 0.5833) X_1520 = ORTHOJOIN OF X(10) (0.6617, 1.1388) A B C X4 X572 X1520 Kimberling (6, 9, 13) | AB = 1 X1520 (ORTHOJOIN OF X10) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 572} Related Centers: X4 (ORTHOCENTER), X572 (ORTHOGONAL OF X58) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-9.099248427634\) ▸ Incident Central Lines1 line {4, 572}