X1643

TRIPOLAR CENTROID OF X105

X1643 is the tripolar centroid of X105.
< 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) { 6, 513 }: Central Line L(6, 513) { 1, 650 }: Central Line L(1, 650) { 42, 663 }: Central Line L(42, 663) { 244, 665 }: Central Line L(244, 665) { 57, 1022 }: Central Line L(57, 1022) { 649, 764 }: Central Line L(649, 764) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1 = INCENTER (0.5714, 0.2333) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1022 = INTERSECTION OF LINES X(1)X(513) AND X(2)X(514) (1.0000, -0.0000) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_764 = TRILINEAR CUBE OF X(513) (1.2143, -0.1166) X_1643 = TRIPOLAR CENTROID OF X(105) (0.8104, 0.1527) A B C X6 X513 X1 X650 X42 X663 X244 X665 X57 X1022 X649 X764 X1643 (a, b, c) = (5, 6, 7) | AB = 1

X1643 (TRIPOLAR CENTROID OF X105) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1635)
Search Value (6, 9, 13): \(-0.010506968202\)
▸ Incident Central Lines6 lines

{1, 650}, {6, 513}, {42, 663}, {57, 1022}, {244, 665}, {649, 764}