← etc / Encyclopedia of Triangle Centers X1601–X1661 · TCC-Perspectors & Tripolar Centroids / X_1604 ← Prev Overview · Code Next → X1604¶ TCC-PERSPECTOR OF X9 X1604 is the tcc-perspector of X9. 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) { 3, 9 }: Central Line L(3, 9) { 25, 1863 }: Central Line L(25, 1863) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_1863 = ZOSMA TRANSFORM OF X(269) (0.6414, 0.4494) X_1604 = TCC-PERSPECTOR OF X(9) (0.3886, -0.5005) A B C X3 X9 X25 X1863 X1604 (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) { 3, 9 }: Central Line L(3, 9) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_9 = MITTENPUNKT (0.5091, 0.1091) X_1604 = TCC-PERSPECTOR OF X(9) (0.3077, -2.3077) A B C X3 X9 X1604 (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) { 3, 9 }: Central Line L(3, 9) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_9 = MITTENPUNKT (0.5077, 0.1103) X_1604 = TCC-PERSPECTOR OF X(9) (0.3365, -2.3381) A B C X3 X9 X1604 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) { 3, 9 }: Central Line L(3, 9) { 25, 1863 }: Central Line L(25, 1863) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_9 = MITTENPUNKT (0.5022, 0.0343) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.5783, 0.3748) X_1863 = ZOSMA TRANSFORM OF X(269) (0.4934, 0.3392) X_1604 = TCC-PERSPECTOR OF X(9) (0.5086, 0.9459) A B C X3 X9 X25 X1863 X1604 Kimberling (6, 9, 13) | AB = 1 X1604 (TCC-PERSPECTOR OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {3, 9}, {25, 1863} Related Centers: X3 (CIRCUMCENTER), X9 (MITTENPUNKT), X25 (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X1863 (ZOSMA TRANSFORM OF X269) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1601) Search Value (6, 9, 13): \(-5.897939752733\) ▸ Incident Central Lines2 lines {3, 9}, {25, 1863} ▸ Functional Relations3 relations X1604 = isogonal conjugate of X34546 X1604 = circumcircle-inverse-of X17112 X1604 = X346-Ceva conjugate of X6