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平面几何题中,由于图形位置关系的不同,学生在解题时往往出现漏解现象。本文仅举几例剖析漏解原因。 一、忽视深挖概念的外延 例1 相切两圆的半径分别是3cm、1cm,则两圆的圆心距为_____。 分析:学生解该题时往往出现漏解,原因是对相切这一概念的外延不清。“相切”包括内切和外切两种情况。两圆内切时,圆心距为2cm;两圆外切时,圆心距为4cm。故正确答案应是2cm或4cm。
In the plane geometry problem, due to the different relationship of the position of the graph, the students often appear to leak when they solve the problem. This article just took a few cases to analyze the cause of the leak. First, ignore the extension of the concept of deep excavation. Example 1 The radius of the tangent two circles is 3cm and 1cm, respectively, and the circle center distance of the two circles is _____. Analysis: When students solve the problem, they often miss the explanation because the extension of the concept of tangency is unclear. “Affinity” includes both in- and out-cuts. When the two circles are inscribed, the center-to-center distance is 2 cm; when the two circles are cut out, the center-to-center distance is 4 cm. Therefore, the correct answer should be 2cm or 4cm.