① Archimedes' chord-folding theorem: It is known that four points A, B, C and D are on the circle O in turn, AB=⌒CD(⌒ stands for arc), BM⊥AC, and the vertical foot is m, which proves that AM=DC+CM.

(2) The chord tangent angle is equal to the circumferential angle of the same arc, and the chord tangent angle on the same arc or equal arc is equal.

③ When the circle is at four o'clock, the diagonal sum is 180.

(4) The product of diagonal lines of quadrilateral inscribed in a circle is equal to the sum of the products of two opposite sides.

⑤ Draw a vertical line from any point P on ABC's circumscribed circle to the straight line where AB, BC and CA are located, and set the vertical ruler as D, E and F respectively, then the straight line of D, E and F***.