First of all, there are three simple and basic theorems: Ptolemy theorem, Menelaus theorem and Seva theorem; Secondly, there are some basics: Butterfly Theorem, siemsen Theorem, Newton Theorem and so on. Again, the marking teacher may not know the theorem, and most of them can't be used directly: Lemoine theorem (crossing the three vertices of a triangle as the tangents of its circumscribed circle, crossing the relative extension line * * *) Carnot theorem (making a point p on the △ABC circumscribed circle, and crossing the point p leads to three sides). ) Qing Palace Theorem (Let P and Q be two points on the circumscribed circle of △ABC that are different from A, B and C, and the symmetry points of P about BC, CA and AB are U, V and W respectively. If Qu, CA and AB intersect with BC, CA and AB or their extension lines are in D, E and F, then D, E and F are on the same straight line. Pascal's theorem (a circle inscribed with the intersection of three pairs of opposite sides of a hexagon (straight line)) Aubert's Theorem (Obel's Theorem) (aubert's Theorem: Draw three parallel lines through the three vertices of △ABC, and their intersections with the circumscribed circle of △ABC are L, M and N respectively. Take a point P from the circumscribed circle of △ABC, then the intersections of PL, PM, PN with BC, CA and AB or their extension lines are D and E respectively. Brian's double theorem (suppose a hexagon is circumscribed by a conic curve, then the connecting line of its three pairs of vertices is * * * points. )。 . . . . . . . . . . . . . . . . . . . Too many. Ask me directly if you have any questions. . . . . .