← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1544 ← Prev Overview · Code Next → X1544¶ ORTHOJOIN OF X58 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, 9 }: Orthocenter–Spieker Line { 30, 113 }: Central Line L(30, 113) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1544 = ORTHOJOIN OF X(58) (-1.1953, -3.7857) A B C X4 X9 X30 X113 X1544 (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, 9 }: Orthocenter–Spieker Line { 30, 113 }: Central Line L(30, 113) 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_9 = MITTENPUNKT (0.5091, 0.1091) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1544 = ORTHOJOIN OF X(58) (-0.1664, -1.8048) A B C X4 X9 X30 X113 X1544 (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, 9 }: Orthocenter–Spieker Line { 30, 113 }: Central Line L(30, 113) 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_9 = MITTENPUNKT (0.5077, 0.1103) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1544 = ORTHOJOIN OF X(58) (-0.0642, -1.8366) A B C X4 X9 X30 X113 X1544 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, 9 }: Orthocenter–Spieker Line { 30, 113 }: Central Line L(30, 113) 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_9 = MITTENPUNKT (0.5022, 0.0343) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1544 = ORTHOJOIN OF X(58) (0.5000, 0.0211) A B C X4 X9 X30 X113 X1544 Kimberling (6, 9, 13) | AB = 1 X1544 (ORTHOJOIN OF X58) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 9}, {30, 113} Related Centers: X4 (ORTHOCENTER), X9 (MITTENPUNKT), X30 (EULER INFINITY POINT), X113 (JERABEK ANTIPODE) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(3.725540923947\) ▸ Incident Central Lines2 lines {4, 9}, {30, 113}
