X1051

POINT ALGORAB

< 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) { 165, 572 }: Central Line L(165, 572) { 1, 748 }: Central Line L(1, 748) { 6, 846 }: Central Line L(6, 846) { 81, 1054 }: Central Line L(81, 1054) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_1 = INCENTER (0.5714, 0.2333) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_1051 = POINT ALGORAB (0.5863, 0.2501) A B C X165 X572 X1 X748 X6 X846 X81 X1054 X1051 (a, b, c) = (5, 6, 7) | AB = 1

X1051 (POINT ALGORAB) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 3a^{2} + b^{2} + c^{2} + bc + 5ab + 5ac\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.318945306191\)
▸ Incident Central Lines4 lines

{1, 748}, {6, 846}, {81, 1054}, {165, 572}