← etc / Encyclopedia of Triangle Centers X1601–X1661 · TCC-Perspectors & Tripolar Centroids / X_1601 ← Prev Overview · Code Next → X1601¶ TCC-PERSPECTOR OF X5 X1601 is the tcc-perspector of X5. 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, 128 }: Central Line L(3, 128) { 6, 1166 }: Central Line L(6, 1166) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1614 = TCC-PERSPECTOR OF X(54) (0.5582, -0.0024) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_128 = -OF-ORTHIC-TRIANGLE (0.3310, 0.3690) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1166 = 1st SARAGOSSA POINT OF X(5) (0.6183, 0.2746) X_1601 = TCC-PERSPECTOR OF X(5) (0.4370, 0.2016) A B C X1614 X3 X128 X6 X1166 X1601 (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, 128 }: Central Line L(3, 128) { 6, 1166 }: Central Line L(6, 1166) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1614 = TCC-PERSPECTOR OF X(54) (0.6400, -0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_128 = -OF-ORTHIC-TRIANGLE (1.4211, 0.8430) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_1166 = 1st SARAGOSSA POINT OF X(5) (0.6719, 0.2330) X_1601 = TCC-PERSPECTOR OF X(5) (0.7387, 0.2184) A B C X1614 X3 X128 X6 X1166 X1601 (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, 128 }: Central Line L(3, 128) { 6, 1166 }: Central Line L(6, 1166) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1614 = TCC-PERSPECTOR OF X(54) (0.6180, -0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_128 = -OF-ORTHIC-TRIANGLE (0.2641, 0.3398) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_1166 = 1st SARAGOSSA POINT OF X(5) (0.6457, 0.2379) X_1601 = TCC-PERSPECTOR OF X(5) (0.2898, 0.3027) A B C X1614 X3 X128 X6 X1166 X1601 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, 128 }: Central Line L(3, 128) { 6, 1166 }: Central Line L(6, 1166) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1614 = TCC-PERSPECTOR OF X(54) (0.4946, 0.9296) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_128 = -OF-ORTHIC-TRIANGLE (0.4234, 0.0307) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_1166 = 1st SARAGOSSA POINT OF X(5) (0.0961, 0.4893) X_1601 = TCC-PERSPECTOR OF X(5) (0.3443, 0.3461) A B C X1614 X3 X128 X6 X1166 X1601 Kimberling (6, 9, 13) | AB = 1 X1601 (TCC-PERSPECTOR OF X5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {3, 128}, {6, 1166} Related Centers: X1614 (TCC-PERSPECTOR OF X54), X3 (CIRCUMCENTER), X128 (-OF-ORTHIC-TRIANGLE), X6 (SYMMEDIAN POINT), X1166 (1st SARAGOSSA POINT OF X5) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1601) Search Value (6, 9, 13): \(1.595948950554\) ▸ Incident Central Lines2 lines {3, 128}, {6, 1166} ▸ Functional Relations2 relations X1601 = X60-of-tangential-triangle if ABC is acute X1601 = tangential isogonal conjugate of X1614
