← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1527 ← Prev Overview · Code Next → X1527¶ ORTHOJOIN OF X18 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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_128 = -OF-ORTHIC-TRIANGLE (0.3310, 0.3690) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.8932, 0.6667) X_1527 = ORTHOJOIN OF X(18) (0.7725, 0.9481) A B C X4 X15 X128 X1154 X1527 (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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5764, 0.1310) X_128 = -OF-ORTHIC-TRIANGLE (1.4211, 0.8430) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.9253, 0.5927) X_1527 = ORTHOJOIN OF X(18) (0.5182, -0.1889) A B C X4 X15 X128 X1154 X1527 (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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.5641, 0.1319) X_128 = -OF-ORTHIC-TRIANGLE (0.2641, 0.3398) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.8780, 0.6266) X_1527 = ORTHOJOIN OF X(18) (0.6835, 0.9151) A B C X4 X15 X128 X1154 X1527 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, 15 }: Central Line L(4, 15) { 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_15 = 1st ISODYNAMIC POINT (0.6000, 0.0051) X_128 = -OF-ORTHIC-TRIANGLE (0.4234, 0.0307) X_1154 = ISOGONAL CONJUGATE OF X(1141) (1.1935, 0.1882) X_1527 = ORTHOJOIN OF X(18) (0.6021, 0.0568) A B C X4 X15 X128 X1154 X1527 Kimberling (6, 9, 13) | AB = 1 X1527 (ORTHOJOIN OF X18) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 15}, {128, 1154} Related Centers: X4 (ORTHOCENTER), X15 (1st 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): \(2.552205025190\) ▸ Incident Central Lines2 lines {4, 15}, {128, 1154}
