Trilinears cos A - cos B cos C : cos B - cos C cos A : cos C - cos A cos B
= sec A - sec B sec C : sec B - sec C sec A : sec C - sec A sec B
Barycentrics tan B + tan C - tan A : tan C + tan A - tan B : tan A + tan B - tan C
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [-3a4 + 2a2(b2 + c2) + (b2 - c2)2]
X(2) is the reflection of X(4) in X(3); also, the orthocenter of the anticomplementary triangle.
X(20) lies on these lines:
1,7 2,3 8,40 10,165 33,1038 34,1040 35,1478 36,1479 55,388 56,497 57,938 58,387 64,69 68,74 72,144 78,329 97,1217 98,148 99,147 100,153 101,152 103,150 104,149 109,151 110,146 145,517 155,323 185,193 190,1265 243,1118 254,1300 346,1766 371,1587 372,1588 391,573 393,577 394,1032 485,1131 486,1132 487,638 488,637 616,633 617,635 621,627 622,628 936,1750 999,1058 1062,1870 1074,1838 1076,1785 1125,1699 1147,1614 1155,1788 1204,1899 1440,1804 1610,1633
X(20) is the {X(3),X(4)}-harmonic conjugate of X(2).
X(20) = reflection of X(I) in X(J) for these (I,J): (2,376), (3,550), (4,3), (5,548), (8,40), (69,1350), (145,944),
(146,110), (147,99), (148,98), (149,104), (150,103), (151,109), (152,101), (153,100), (382,5), (962,1)
X(20) = isogonal conjugate of X(64)
X(20) = isotomic conjugate of X(253)
X(20) = cyclocevian conjugate of X(1032)
X(20) = inverse-in-circumcircle of X(2071)
X(20) = inverse-in-orthocentroidal-circle of X(3091)
X(20) = complement of X(3146)
X(20) = anticomplement of X(4)
X(20) = anticomplementary conjugate of X(4)
X(20) = X(I)-Ceva conjugate of X(J) for these (I,J): (69,2), (489,487), (490,488)
X(20) = crosssum of X(1) and X(1044)
X(20) = crossdifference of any two points on line X(647)X(657)
X(20) = X(I)-aleph conjugate of X(J) for these (I,J): (8,191), (9,1045), (188,1046), (333,2), (1043,20)
X(20) = X(I)-beth conjugate of X(J) for these (I,J): (664,20), (1043,280)
, select the center name from the list and, then, click on the vertices A, B and C successively.