← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1525 ← Prev Overview · Code Next → X1525¶ ORTHOJOIN OF X16 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, 14 }: Central Line L(4, 14) { 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_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_1525 = ORTHOJOIN OF X(16) (0.4851, 0.6110) A B C X4 X14 X30 X113 X1525 (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, 14 }: Central Line L(4, 14) { 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_14 = 2nd ISOGONIC CENTER (0.8701, -0.1545) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_1525 = ORTHOJOIN OF X(16) (0.5624, 0.6940) A B C X4 X14 X30 X113 X1525 (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, 14 }: Central Line L(4, 14) { 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_14 = 2nd ISOGONIC CENTER (0.8270, -0.1871) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_1525 = ORTHOJOIN OF X(16) (0.5518, 0.6991) A B C X4 X14 X30 X113 X1525 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, 14 }: Central Line L(4, 14) { 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_14 = 2nd ISOGONIC CENTER (0.7495, -0.2320) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_1525 = ORTHOJOIN OF X(16) (0.6162, 0.9844) A B C X4 X14 X30 X113 X1525 Kimberling (6, 9, 13) | AB = 1 X1525 (ORTHOJOIN OF X16) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 14}, {30, 113} Related Centers: X4 (ORTHOCENTER), X14 (2nd ISOGONIC CENTER), 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): \(-7.143811975243\) ▸ Incident Central Lines2 lines {4, 14}, {30, 113} ▸ Functional Relations1 relation X1525 = reflection of Xi in Xj for these (i,j): (1524, 1514), (1545, 1524)
