X1283

7th SHARYGIN POINT

X1283 is the center of similitude of the triangles DEF and D'E'F' constructed at X1281. Coordinates were found by Jean-Pierre Ehrmann. See Hyacinthos #6293 and #6315.
< 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) circumcircle: Circumcircle of △ABC { 3, 1054 }: Central Line L(3, 1054) { 10, 21 }: Central Line L(10, 21) { 36, 244 }: Central Line L(36, 244) { 242, 243 }: Central Line L(242, 243) { 55, 846 }: Central Line L(55, 846) 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_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_1283 = 7th SHARYGIN POINT (0.7481, 0.0125) A B C X3 X1054 X10 X21 X36 X244 X242 X243 X55 X846 X1283 (a, b, c) = (5, 6, 7) | AB = 1

X1283 (7th SHARYGIN POINT) 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 \(f(a,b,c) = a[a^{4} - (b + c)a^{3} + (b^{3} + c^{3})a + b^{2}c^{2} - b^{4} - c^{4}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.985662986109\)
▸ Incident Central Lines5 lines

{3, 1054}, {10, 21}, {36, 244}, {55, 846}, {242, 243}

▸ Functional Relations2 relations