论文部分内容阅读
2008高考.我最欣赏的一道数学试题是江西卷理科第10题.试题如下.连接球面上两点的线段称为球的弦.如下图,半径为4的球的两条弦AB、CD的长度分别等于2 7~(1/2)、4 3~(1/2),M,N分别为AB、CD的中点,每条弦的两端都在球面上运动,有下列四个命题:①弦AB、CD可能相交于点M②弦AB、CD可能相交于点N③MN的最大值为5④MN的最小值为1其中真命题的个数为( ).
2008 college entrance examination. One of my favorite mathematics questions is the 10th item in the Jiangxi Science and Technology Division. The questions are as follows. The line connecting two points on the sphere is called the string of the ball. As shown in the figure below, the two strings of the ball with radius 4 are AB and CD. The lengths are equal to 2 7~(1/2) and 4 3~(1/2), respectively. M and N are the midpoints of AB and CD respectively. Both ends of each string move on the sphere. There are the following four propositions. :1 The chords AB and CD may intersect at the point M2 The chords AB and CD may intersect at the point N3MN The minimum value of 54MN is 1 where the number of true propositions is ().