← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1547 ← Prev Overview · Code Next → X1547¶ ORTHOJOIN OF X71 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, 6 }: Van Aubel 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_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) 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_1547 = ORTHOJOIN OF X(71) (0.6764, 1.0690) A B C X4 X6 X118 X516 X1547 (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, 6 }: Van Aubel 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_4 = ORTHOCENTER (0.6400, 0.4800) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) 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_1547 = ORTHOJOIN OF X(71) (0.6400, 0.9415) A B C X4 X6 X118 X516 X1547 (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, 6 }: Van Aubel 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_4 = ORTHOCENTER (0.6180, 0.4859) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) 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_1547 = ORTHOJOIN OF X(71) (0.6180, 0.9584) A B C X4 X6 X118 X516 X1547 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, 6 }: Van Aubel 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_4 = ORTHOCENTER (0.6331, 0.8294) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) 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_1547 = ORTHOJOIN OF X(71) (0.6244, 1.0697) A B C X4 X6 X118 X516 X1547 Kimberling (6, 9, 13) | AB = 1 X1547 (ORTHOJOIN OF X71) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 6}, {118, 516} Related Centers: X4 (ORTHOCENTER), X6 (SYMMEDIAN POINT), 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): \(-8.090240796620\) ▸ Incident Central Lines2 lines {4, 6}, {118, 516}
