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2015年7月,笔者有幸参与了连云港市2015年中考阅卷工作,批阅数学卷第24题.阅卷过程中,笔者发现考生在该题上的一类典型错误对教学工作具有一定的启示意义.将其整理成文,期望能对同行有所助益.一、题目及考生的一类典型错识题目:(连云港2015第24题)已知如图,在平面直角坐标系xOy中,直线y=3~(1/2)-2 3~(1/2)与x轴、y轴分别交于A、B两点,P是直线AB上一动点,⊙P的半径为1.(1)判断原点O与⊙P的位置关系,并说明理由;(2)当⊙P过点B时,求⊙P被y轴所截得的劣弧的长;(3)当⊙P与x轴相切时,求出切点的坐标.
July 2015, I was fortunate enough to participate in the Lianyungang City in 2015 examination paperwork, access to mathematics volume 24 questions.While marking process, I found that the candidates on the subject of a class of typical mistakes on the teaching work has some enlightenment significance The collation, in the hope of benefiting the colleague.One, the subject and a typical class of erroneous subjects: (Lianyungang2015 24) Known as shown in the plane Cartesian coordinate system xOy, the straight line y = 3 ~ (1/2) -2 3 ~ (1/2) and the x-axis and y-axis are respectively intersected with point A and point B. P is the last point of the line AB, and the radius of ⊙P is 1. (1) O and ⊙ P, and explain the reason; (2) When ⊙ P over point B, find ⊙ P by the y axis of the interception of the length of the poor arc; (3) ⊙ P tangent to the x axis , Find the coordinates of the point of contact.