圆的垂径定理:垂直于弦的直径平分这条弦.这个定理有不少的应用.请看以下五例:例1如图1,已知AC、BD是⊙O的内接四边形ABCD的对角线,且BD垂直平分半径OC,在AC上取一点P使CP=OC,连结BP并延长交AD于点E,交⊙O于点F.求证PF是EF和BF的比例中项.(04年荆州市初数竞) The vertical path theorem: perpendicular to the diameter of the chord bisect the chord. There are many applications for this theorem. See the following five examples: Example 1 As shown in Figure 1, AC and BD are known as the inscribed quadrilateral ABCD of ⊙O. Diagonal, and BD vertically divides the radius OC, take a point P on AC to make CP=OC, link BP and extend AD to point E, and intersect O at point F. Prove that PF is the proportion of EF and BF. (Opening of Jingzhou City in 2004)