← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1521 ← Prev Overview · Code Next → X1521¶ ORTHOJOIN OF X11 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) { 117, 515 }: Central Line L(117, 515) { 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_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) 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_1521 = ORTHOJOIN OF X(11) (0.5709, 0.8250) A B C X117 X515 X118 X516 X1521 (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) { 117, 515 }: Central Line L(117, 515) { 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_117 = MIDPOINT OF X(4) AND X(109) (0.5700, 0.4900) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6280, 0.7292) 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_1521 = ORTHOJOIN OF X(11) (0.6308, 0.9154) A B C X117 X515 X118 X516 X1521 (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) { 117, 515 }: Central Line L(117, 515) { 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_117 = MIDPOINT OF X(4) AND X(109) (0.5590, 0.4929) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6077, 0.7329) 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_1521 = ORTHOJOIN OF X(11) (0.6125, 0.9395) A B C X117 X515 X118 X516 X1521 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) { 117, 515 }: Central Line L(117, 515) { 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_117 = MIDPOINT OF X(4) AND X(109) (0.6190, 0.5577) X_515 = ISOGONAL CONJUGATE OF X(102) (0.5610, 0.7492) 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_1521 = ORTHOJOIN OF X(11) (0.6334, 1.1242) A B C X117 X515 X118 X516 X1521 Kimberling (6, 9, 13) | AB = 1 X1521 (ORTHOJOIN OF X11) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {117, 515}, {118, 516} Related Centers: X117 (MIDPOINT OF X4 AND X109), X515 (ISOGONAL CONJUGATE OF X102), 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): \(-8.724479724155\) ▸ Incident Central Lines2 lines {117, 515}, {118, 516}