← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1528 ← Prev Overview · Code Next → X1528¶ ORTHOJOIN OF X19 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) { 1, 4 }: Incenter–Orthocenter Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1528 = ORTHOJOIN OF X(19) (0.5409, 0.1119) A B C X1 X4 X1528 (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) { 1, 4 }: Incenter–Orthocenter Line { 2, 3 }: Euler Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1 = INCENTER (0.6000, 0.2000) X_4 = ORTHOCENTER (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_1528 = ORTHOJOIN OF X(19) (0.6400, 0.4800) A B C X1 X4 X2 X3 X1528 (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) { 1, 4 }: Incenter–Orthocenter Line { 2, 3 }: Euler Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1 = INCENTER (0.5841, 0.2021) X_4 = ORTHOCENTER (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_1528 = ORTHOJOIN OF X(19) (0.6180, 0.4859) A B C X1 X4 X2 X3 X1528 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) { 1, 4 }: Incenter–Orthocenter Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1 = INCENTER (0.6154, 0.1300) X_4 = ORTHOCENTER (0.6331, 0.8294) X_1528 = ORTHOJOIN OF X(19) (0.6356, 0.9279) A B C X1 X4 X1528 Kimberling (6, 9, 13) | AB = 1 X1528 (ORTHOJOIN OF X19) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {1, 4} Related Centers: X1 (INCENTER), X4 (ORTHOCENTER) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-6.714127885523\) ▸ Incident Central Lines1 line {1, 4}