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证明直线是圆的切线的问题在近几年的中考中出现较多,但因其条件不一,证明方法也不同,同学们不易把握,直线和圆相切的判定方法一般可分为两种,现总结如下:方法一:由条件可以判断直线与圆有公共端点时,连接该公共端点和圆心,证明该半径垂直已知直线。例1(2013·江苏泰州)如图1,AB为⊙O的直径,AC、DC为弦,∠ACD=60°,P为AB延长线上的点,∠APD=30°。求证:DP是⊙O的切线。
The problem of proving that a straight line is a tangent to a circle appears more in the senior high school entrance examinations in recent years. However, due to different conditions and different methods of proof, students are not easy to grasp. The methods for determining the tangent of a straight line and a circle can be generally divided into two types , Are summarized as follows: Method one: the conditions can be judged straight line and the circle has a common endpoint, the connection of the common endpoint and the center of the circle, that radius of the vertical known line. Example 1 (2013 · Taizhou, Jiangsu) As shown in Figure 1, AB is the diameter of ⊙O, AC, DC is chord, ∠ACD = 60 °, P is the point on AB extension line, ∠APD = 30 °. Prove: DP is the tangent of ⊙ O.