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X(5051) lies on these lines: 1, 3454, 2, 3, 8, 1211, 10, good christmas gift ideas for my dad 321, 12, 1284, 45, 1213, 75, 1228, 81, 1330, 115, 1281, 225, 1441, 846, 1698, 984, 4812, 1046, 4683, 1193, 3847, 1230, 4385, 1962, 3178, 2298, 4645, 2901, irena nobel prize 3969, 3017, 3578, 3214, 4085.
The centers of those 3 are collinear.
A method for converting from homogeneous tripolar coordinates (henceforth simply "tripolars to homogeneous barycentrics, found by Peter Moses (March, 2012 depends on finding the point of intersection of the radical axes of radical circles centered at A, B,.
The center W of (W,w) is the combo uV vU; that is, barycentrics for W are given by u(vA, vB, vC) v(uA, uB, uC where (uA, uB, uC) are normalized barycentrics for U, and (vA, vB, vC) are normalized barycentrics for. (Peter Moses, October 4, 2013) Let A'B'C' be the cevian triangle of X(3).Nevertheless, for all triangles ABC, the midpoint of X(5002) and X(5003) is X(858).Let MA lcdb, and define MB and MC cyclically.Get your reading now by clicking the angel Want to exchange links with us? (Peter Moses, June 16, 2013) The appearance of (i,j) in the following list means that Q(X(i) X(j (36, 40 (46, 2077 (74, 3464 (100,1054 (105,1282 (109, 1768 (165, 1155 (759, 2948 (1381, 2449 (1382, 2448) (Randy Hutson, July 19, 2013) Let O denote.Note that O Euler line) X(4 X(1316) and O Brocard circle) X(6 X(1316 X(5480) X(6) of Euler triangle; X(5480) X(5478 X(5479)-harmonic conjugate of X(3845 The orthosymmedial circle is the inverse-in-polar-circle of the line X(297)X(525).
Then AC2 BC1, BA1 CA2, CB1 AB2, so that by Carnot's theorem, the six points A1, A2, B1, B2, C1, C2 lie on a conic, named in honor of Alexander Privalov.
The lines AA BB CC' concur in X(5408).
Let DEF be the orthic triangle of ABC.
For a construction and derivation of barycentric coordinates by Shi Yong, see Problem 20 at Unsolved Problems and Rewards.
It is tangent to the Euler line at X(2) and is the reflection in the Euler line of the circle X(2 X(13 X(14 X(111 X(476).The lines AA BB CC* concur in X(5411).A barycentric equation for this 2nd Grigoriev conic follows: x2 y2 z2- 2 sec(A/2) yz - 2 sec(B/2) zx - 2 sec(C/2) xy 0 The perspector of the 2nd Grigoriev conic is X(5451). .X(5129) lies on these lines: 2, 3, 8, 3305, 9, 938, 10, 390, 144, 942, 145, 392, 388, 4423, 519, 4866, 908, 3616, 936, 4313, 1001, 2551, 1125, 3600, 1330, 4869, 1698, 4294, 1788, 3683, 2899, 3757, 3189, 3740, 3241, 3984, 3485, 4679, 3624, 4293.Also, A' is the center of inverse similitude of ABC and the A-altimedial triangle, and cyclically for B' and C'.


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