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一、问题出在哪里?这是一节关于几何概型(人教社高中数学必修3)的习题课,在回顾了几何概型的概念和几何概型中事件A的概率的计算公式之后,作为课堂探究与研讨,我在黑板上写下这样一道题:(2011·湖南高考改编)已知圆C:x2+y2=12,直线l:4x+3y=25.(1)求圆C的圆心到直线l的距离;(2)求圆C上任意一点A到直线l的距离不大于2的概率.六个小组经过积极研讨后,有一个小组未能得出完整结果,其余五个提交了各自的解答.其中有两个小组的解答如下:
First, where is the problem? This is an exercise class on Geometry Outline (compared to the compulsory 3 in Senior High School mathematics). After reviewing the concept of geometric outlines and the calculation formula for the probability of event A in the geometric outline, As a classroom inquiry and discussion, I wrote on the blackboard such a question: (2011 · Hunan college entrance examination adaptation) known circle C: x2 + y2 = 12, the line l: 4x + 3y = 25. (1) find the circle C The distance from the center of the circle to the straight line l; (2) Find the probability that the distance from any point A on the circle C to the straight line l is not greater than 2. After the active discussion among the six groups, one group failed to reach a complete result, and the remaining five were submitted. The respective answers. There are two groups of solutions as follows: