← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1526 ← Prev Overview · Code Next → X1526¶ ORTHOJOIN OF X17 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, 16 }: Central Line L(4, 16) { 128, 1154 }: Central Line L(128, 1154) 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_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_128 = -OF-ORTHIC-TRIANGLE (0.3310, 0.3690) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.8932, 0.6667) X_1526 = ORTHOJOIN OF X(17) (1.9704, 2.5196) A B C X4 X16 X128 X1154 X1526 (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, 16 }: Central Line L(4, 16) { 128, 1154 }: Central Line L(128, 1154) 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_16 = 2nd ISODYNAMIC POINT (1.3303, 1.4234) X_128 = -OF-ORTHIC-TRIANGLE (1.4211, 0.8430) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.9253, 0.5927) X_1526 = ORTHOJOIN OF X(17) (-1.7273, -2.7552) A B C X4 X16 X128 X1154 X1526 (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, 16 }: Central Line L(4, 16) { 128, 1154 }: Central Line L(128, 1154) 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_16 = 2nd ISODYNAMIC POINT (1.2449, 1.5332) X_128 = -OF-ORTHIC-TRIANGLE (0.2641, 0.3398) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.8780, 0.6266) X_1526 = ORTHOJOIN OF X(17) (1.7553, 2.3859) A B C X4 X16 X128 X1154 X1526 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, 16 }: Central Line L(4, 16) { 128, 1154 }: Central Line L(128, 1154) 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_16 = 2nd ISODYNAMIC POINT (0.8687, 0.7568) X_128 = -OF-ORTHIC-TRIANGLE (0.4234, 0.0307) X_1154 = ISOGONAL CONJUGATE OF X(1141) (1.1935, 0.1882) X_1526 = ORTHOJOIN OF X(17) (2.3231, 0.3083) A B C X4 X16 X128 X1154 X1526 Kimberling (6, 9, 13) | AB = 1 X1526 (ORTHOJOIN OF X17) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 16}, {128, 1154} Related Centers: X4 (ORTHOCENTER), X16 (2nd ISODYNAMIC POINT), X128 (-OF-ORTHIC-TRIANGLE), X1154 (ISOGONAL CONJUGATE OF X1141) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-13.622495364493\) ▸ Incident Central Lines2 lines {4, 16}, {128, 1154}
