圆的切线的判定有两个要素:(1)经过半径的外端点;(2)垂直于这条半径.在证明一条直线是圆的切线时,常用的方法有:(1)作半径,证垂直;(2)作垂线,证半径.下面举例说明,希望同学们能够掌握技巧,触类旁通,提高解题技能.例1如图1所示,已知AB是⊙O的直径,线段AE与⊙O相切于点A,D是AE的中点,BE交⊙O于C.求证:CD与⊙O相切于C点.分析:DC与⊙O有公共点C,连结OC,要证DC是⊙O的切线,需证∠DCO=90°.易推∠EAB=90°,因此需证∠DCO=∠DAO.证法1:如图1,连结OC、OD.在⊙O中,因为OA=OB,AD The determination of a circle tangent has two elements: (1) through the outer end point of the radius; (2) perpendicular to this radius. When it is proved that a straight line is a tangent to a circle, the commonly used methods are: (1) As a radius, Vertical; (2) for the vertical line, card radius. The following example shows, I hope the students can master the skills, comprehend by analogy, improve the problem-solving skills. Example 1 shown in Figure 1, known AB is the diameter of ⊙O, line AE and ⊙O is tangential to point A, D is the midpoint of AE, and BE is ⊙O to C. Proof: CD and ⊙O are tangent to point C. Analysis: DC and ⊙O have a common point C, which connects OC. DC is the tangent of ⊙O. It is necessary to prove that DCO is 90°. It is easy to push EAB=90°. Therefore, it is necessary to verify that DCO=∠DAO. Proof 1. As shown in Figure 1, link OC and OD. Because OA = OB, AD