← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1541 ← Prev Overview · Code Next → X1541¶ ORTHOJOIN OF X55 X1541 = orthopole of Gergonne line 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 { 118, 516 }: Central Line L(118, 516) 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_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1541 = ORTHOJOIN OF X(55) (0.9271, 1.6491) A B C X1 X4 X118 X516 X1541 (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 { 118, 516 }: Central Line L(118, 516) 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_118 = MIDPOINT OF X(4) AND X(101) (0.4738, 0.4708) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7380, 0.7022) X_1541 = ORTHOJOIN OF X(55) (0.7508, 1.2554) A B C X1 X4 X118 X516 X1541 (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 { 118, 516 }: Central Line L(118, 516) 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_118 = MIDPOINT OF X(4) AND X(101) (0.4773, 0.4792) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7014, 0.7136) X_1541 = ORTHOJOIN OF X(55) (0.7135, 1.2835) A B C X1 X4 X118 X516 X1541 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 { 118, 516 }: Central Line L(118, 516) 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_118 = MIDPOINT OF X(4) AND X(101) (0.5407, 0.5614) X_516 = ISOGONAL CONJUGATE OF X(103) (0.6510, 0.7407) X_1541 = ORTHOJOIN OF X(55) (0.6419, 1.1763) A B C X1 X4 X118 X516 X1541 Kimberling (6, 9, 13) | AB = 1 X1541 (ORTHOJOIN OF X55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {1, 4}, {118, 516} Related Centers: X1 (INCENTER), X4 (ORTHOCENTER), X118 (MIDPOINT OF X4 AND X101), X516 (ISOGONAL CONJUGATE OF X103) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-9.330720062313\) ▸ Incident Central Lines2 lines {1, 4}, {118, 516} ▸ Functional Relations1 relation X1541 = orthopole of Gergonne line
