← etc / Encyclopedia of Triangle Centers X1601–X1661 · TCC-Perspectors & Tripolar Centroids / X_1641 ← Prev Overview · Code Next → X1641¶ TRIPOLAR CENTROID OF X99 X1641 is the tripolar centroid of X99. 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) { 1648, 2 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 351, 690 }: Central Line L(351, 690) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1648 = TRIPOLAR CENTROID OF X(523) (-0.6135, -1.0369) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_351 = CENTER OF THE PARRY CIRCLE (1.3537, 1.1619) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0840, -0.1726) X_1641 = TRIPOLAR CENTROID OF X(99) (1.6884, 1.4368) A B C X1648 X2 X6 X351 X690 X1641 (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) { 1648, 2 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 351, 690 }: Central Line L(351, 690) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1648 = TRIPOLAR CENTROID OF X(523) (-0.2365, -0.5113) X_2 = CENTROID (0.5467, 0.1600) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_351 = CENTER OF THE PARRY CIRCLE (1.0952, 0.6944) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0500, -0.1297) X_1641 = TRIPOLAR CENTROID OF X(99) (1.3299, 0.8313) A B C X1648 X2 X6 X351 X690 X1641 (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) { 1648, 2 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 351, 690 }: Central Line L(351, 690) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1648 = TRIPOLAR CENTROID OF X(523) (0.1708, -0.2173) X_2 = CENTROID (0.5393, 0.1620) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_351 = CENTER OF THE PARRY CIRCLE (1.2060, 0.6861) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0222, -0.0893) X_1641 = TRIPOLAR CENTROID OF X(99) (0.9079, 0.5412) A B C X1648 X2 X6 X351 X690 X1641 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) { 1648, 2 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 351, 690 }: Central Line L(351, 690) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1648 = TRIPOLAR CENTROID OF X(523) (0.2822, -0.0741) X_2 = CENTROID (0.5444, 0.0934) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_351 = CENTER OF THE PARRY CIRCLE (0.9667, 0.2979) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (-0.0947, -0.0548) X_1641 = TRIPOLAR CENTROID OF X(99) (0.8066, 0.2608) A B C X1648 X2 X6 X351 X690 X1641 Kimberling (6, 9, 13) | AB = 1 X1641 (TRIPOLAR CENTROID OF X99) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {1648, 2} Related Centers: X1648 (TRIPOLAR CENTROID OF X523), X2 (CENTROID) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1635) Search Value (6, 9, 13): \(-1.169284701363\) ▸ Incident Central Lines2 lines {2, 6}, {351, 690} ▸ Functional Relations4 relations X1641 = reflection of X1648 in X2 X1641 = centroid of line X2X6 intercepts with sidelines of ABC X1641 = intersection of tangents to circle {X2,X110,X2770,X5463,X5464} at X5463 and X5464 X1641 = centroid of degenerate cross-triangle of anticomplementary and Schroeter triangles
