← etc / Encyclopedia of Triangle Centers X1908–X2000 · Bicentric Pairs PU(k) & Orthocorrespondents / X_1996 ← Prev Overview · Code Next → X1996¶ ORTHOCORRESPONDENT OF X7 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) { 7, 11 }: Central Line L(7, 11) { 2, 85 }: Central Line L(2, 85) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_7 = GERGONNE POINT (0.5903, 0.2769) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_2 = CENTROID (0.5374, 0.2000) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_1996 = ORTHOCORRESPONDENT OF X(7) (0.5849, 0.2847) A B C X7 X11 X2 X85 X1996 (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) { 7, 11 }: Central Line L(7, 11) { 2, 85 }: Central Line L(2, 85) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_7 = GERGONNE POINT (0.6218, 0.2618) X_11 = FEUERBACH POINT (0.7200, 0.0400) X_2 = CENTROID (0.5467, 0.1600) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5801, 0.2201) X_1996 = ORTHOCORRESPONDENT OF X(7) (0.6136, 0.2803) A B C X7 X11 X2 X85 X1996 (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) { 7, 11 }: Central Line L(7, 11) { 2, 85 }: Central Line L(2, 85) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_7 = GERGONNE POINT (0.6026, 0.2652) X_11 = FEUERBACH POINT (0.6897, 0.0298) X_2 = CENTROID (0.5393, 0.1620) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5676, 0.2231) X_1996 = ORTHOCORRESPONDENT OF X(7) (0.5957, 0.2840) A B C X7 X11 X2 X85 X1996 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) { 7, 11 }: Central Line L(7, 11) { 2, 85 }: Central Line L(2, 85) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_7 = GERGONNE POINT (0.6288, 0.2114) X_11 = FEUERBACH POINT (0.6563, 0.0066) X_2 = CENTROID (0.5444, 0.0934) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5911, 0.1796) X_1996 = ORTHOCORRESPONDENT OF X(7) (0.6247, 0.2415) A B C X7 X11 X2 X85 X1996 Kimberling (6, 9, 13) | AB = 1 X1996 (ORTHOCORRESPONDENT OF X7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {7, 11}, {2, 85} Related Centers: X7 (GERGONNE POINT), X11 (FEUERBACH POINT), X2 (CENTROID), X85 (ISOTOMIC CONJUGATE OF X9) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X7 Search Value (6, 9, 13): \(0.464935011230\) ▸ Incident Central Lines2 lines {2, 85}, {7, 11}
