![](https://wkrtcs.bdimg.com/rtcs/image?w=34.666666666667&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"34.666666666667","h":"49.333333333333","dataType":"png","c":"word/media/image1.png","imgOriW":26,"imgOriH":37})
天津市部分区2017～2018学年度第一学期期末考试
高二数学（理科）参考答案
一、选择题：本大题共10小题，每小题4分，共40分．
题号 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
答案 | C | B | B | A | A | D | A | B | C | D |
二、填空题：本大题共5小题，每小题4分，共20分．
11．![](https://wkrtcs.bdimg.com/rtcs/image?w=45&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"45","h":"21","dataType":"gif","c":"word/media/image10.png"})
12． 13． 14． 15.
三、解答题：本大题共5小题，共60分．解答应写出文字说明、证明过程或演算步骤．
16．（12分）
解：（1）由题意知![](https://wkrtcs.bdimg.com/rtcs/image?w=163&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"163","h":"29","dataType":"gif","c":"word/media/image15.png"})
，解得.……………4分
（2）当![](https://wkrtcs.bdimg.com/rtcs/image?w=37&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"37","h":"19","dataType":"gif","c":"word/media/image17.png"})
时,由
得![](https://wkrtcs.bdimg.com/rtcs/image?w=137&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"137","h":"29","dataType":"gif","c":"word/media/image19.png"})
，………………………………………………………6分
所以圆心坐标为![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"43","h":"21","dataType":"gif","c":"word/media/image20.png"})
，半径，
圆心到直线![](https://wkrtcs.bdimg.com/rtcs/image?w=83&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"83","h":"21","dataType":"gif","c":"word/media/image22.png"})
的距离为，……………………8分
所以弦长的一半![](https://wkrtcs.bdimg.com/rtcs/image?w=133&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"133","h":"40","dataType":"gif","c":"word/media/image24.png"})
………………………………………10分
![](https://wkrtcs.bdimg.com/rtcs/image?w=15&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"15","h":"13","dataType":"gif","c":"word/media/image25.png"})
弦长为……………………………………………………………………12分
17．（12分）
解：（1）由方程![](https://wkrtcs.bdimg.com/rtcs/image?w=53&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"53","h":"24","dataType":"gif","c":"word/media/image27.png"})
， 消去后，整理得
设![](https://wkrtcs.bdimg.com/rtcs/image?w=59&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"59","h":"24","dataType":"gif","c":"word/media/image31.png"})
，由韦达定理,，……………2分
∵![](https://wkrtcs.bdimg.com/rtcs/image?w=32&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"32","h":"21","dataType":"gif","c":"word/media/image35.png"})
在抛物线上，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=59&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"59","h":"25","dataType":"gif","c":"word/media/image36.png"})
,，∴.…………………………4分
∵![](https://wkrtcs.bdimg.com/rtcs/image?w=129&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"129","h":"45","dataType":"gif","c":"word/media/image39.png"})
，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=77&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"77","h":"41","dataType":"gif","c":"word/media/image40.png"})
……………………………………………………………………6分
（2）因为![](https://wkrtcs.bdimg.com/rtcs/image?w=49&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"49","h":"23","dataType":"gif","c":"word/media/image41.png"})
，由（1）可得，代入抛物线方程可得
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=69&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"69","h":"32","dataType":"gif","c":"word/media/image44.png"})
， ……………………………………………………9分
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=269&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"269","h":"41","dataType":"gif","c":"word/media/image46.png"})
………………………………12分
18．（12分）
解：（1）证明：在![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"48","h":"17","dataType":"gif","c":"word/media/image47.png"})
中，∵，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=120&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"120","h":"20","dataType":"gif","c":"word/media/image49.png"})
∴．……………………………………………………3分
又∵平面![](https://wkrtcs.bdimg.com/rtcs/image?w=37&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"37","h":"17","dataType":"gif","c":"word/media/image51.png"})
⊥平面，平面平面，
![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"43","h":"17","dataType":"gif","c":"word/media/image55.png"})
面，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=41&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"41","h":"17","dataType":"gif","c":"word/media/image56.png"})
面，又面，
∴平面![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"40","h":"17","dataType":"gif","c":"word/media/image58.png"})
⊥平面．………………………6分
![](https://wkrtcs.bdimg.com/rtcs/image?w=192.86666666667&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"192.86666666667","h":"165.13333333333","dataType":"emf","c":"word/media/image59.png"})
（2）解：过作，
∵平面⊥平面，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"27","h":"19","dataType":"gif","c":"word/media/image62.png"})
⊥平面，
即为四棱锥的高．
又![](https://wkrtcs.bdimg.com/rtcs/image?w=47&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"47","h":"17","dataType":"gif","c":"word/media/image64.png"})
是边长为的等边三角形，
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=63&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"63","h":"24","dataType":"gif","c":"word/media/image66.png"})
．………………………9分
在底面四边形![](https://wkrtcs.bdimg.com/rtcs/image?w=48&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"48","h":"19","dataType":"gif","c":"word/media/image52.png"})
中，，，
在![](https://wkrtcs.bdimg.com/rtcs/image?w=61&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"61","h":"19","dataType":"gif","c":"word/media/image69.png"})
中，斜边边上的高为，
此即为![](https://wkrtcs.bdimg.com/rtcs/image?w=47&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"47","h":"19","dataType":"gif","c":"word/media/image72.png"})
的高．
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=165&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"165","h":"45","dataType":"gif","c":"word/media/image73.png"})
．…………………11分
∴![](https://wkrtcs.bdimg.com/rtcs/image?w=169&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"169","h":"45","dataType":"gif","c":"word/media/image74.png"})
．…………………12分
19．解：（12分）
![](https://wkrtcs.bdimg.com/rtcs/image?w=120.13333333333&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"120.13333333333","h":"108.66666666667","dataType":"png","c":"word/media/image75.png","imgOriW":920,"imgOriH":833})
（1）证明：以为原点，建立如图所示的空间直角坐标系，设,则，，，，
![](https://wkrtcs.bdimg.com/rtcs/image?w=64&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"64","h":"27","dataType":"gif","c":"word/media/image83.png"})
, ,，，
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=109&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"109","h":"28","dataType":"gif","c":"word/media/image87.png"})
,，
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=85&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"85","h":"28","dataType":"gif","c":"word/media/image89.png"})
，所以.……………………3分
（2）由![](https://wkrtcs.bdimg.com/rtcs/image?w=83&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"83","h":"28","dataType":"gif","c":"word/media/image91.png"})
,则，连接，所以，，，
设平面![](https://wkrtcs.bdimg.com/rtcs/image?w=41&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"41","h":"24","dataType":"gif","c":"word/media/image97.png"})
的法向量为， 则，取
所以平面的一个法向量为，
因为![](https://wkrtcs.bdimg.com/rtcs/image?w=41&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"41","h":"17","dataType":"gif","c":"word/media/image103.png"})
平面，所以，即，所以.……7分
（3）连接![](https://wkrtcs.bdimg.com/rtcs/image?w=28&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"28","h":"24","dataType":"gif","c":"word/media/image107.png"})
，，设平面的法向量为，，，
则![](https://wkrtcs.bdimg.com/rtcs/image?w=149&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"149","h":"59","dataType":"gif","c":"word/media/image113.png"})
,取
所以平面![](https://wkrtcs.bdimg.com/rtcs/image?w=40&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"40","h":"24","dataType":"gif","c":"word/media/image109.png"})
的一个法向量为 ……………………9分
因为二面角![](https://wkrtcs.bdimg.com/rtcs/image?w=84&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"84","h":"24","dataType":"gif","c":"word/media/image116.png"})
的大小为，
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=43&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"43","h":"24","dataType":"gif","c":"word/media/image118.png"})
，所以，
因为![](https://wkrtcs.bdimg.com/rtcs/image?w=37&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"37","h":"19","dataType":"gif","c":"word/media/image120.png"})
，所以，即.……………………12分
20．（12分）
解：（1）由题意可得![](https://wkrtcs.bdimg.com/rtcs/image?w=65&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"65","h":"41","dataType":"gif","c":"word/media/image123.png"})
, ,又，解得.
所以所求椭圆![](https://wkrtcs.bdimg.com/rtcs/image?w=16&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"16","h":"19","dataType":"gif","c":"word/media/image127.png"})
的方程为.……………………………………3分
（2）设，
由![](https://wkrtcs.bdimg.com/rtcs/image?w=84&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"84","h":"69","dataType":"gif","c":"word/media/image129.png"})
消去得，
![](https://wkrtcs.bdimg.com/rtcs/image?w=241&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"241","h":"29","dataType":"gif","c":"word/media/image132.png"})
,化为.
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=109&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"109","h":"41","dataType":"gif","c":"word/media/image134.png"})
，.…………………………7分
![](https://wkrtcs.bdimg.com/rtcs/image?w=343&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"343","h":"27","dataType":"gif","c":"word/media/image136.png"})
.
因为以![](https://wkrtcs.bdimg.com/rtcs/image?w=27&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"27","h":"17","dataType":"gif","c":"word/media/image70.png"})
为直径的圆过椭圆右顶点，，
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=120&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"120","h":"45","dataType":"gif","c":"word/media/image140.png"})
， 所以，
所以![](https://wkrtcs.bdimg.com/rtcs/image?w=256&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"256","h":"44","dataType":"gif","c":"word/media/image142.png"})
.
化为![](https://wkrtcs.bdimg.com/rtcs/image?w=143&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"143","h":"21","dataType":"gif","c":"word/media/image143.png"})
，
解得![](https://wkrtcs.bdimg.com/rtcs/image?w=132&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"132","h":"41","dataType":"gif","c":"word/media/image144.png"})
.……………………………………………10分
且满足![](https://wkrtcs.bdimg.com/rtcs/image?w=83&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"83","h":"21","dataType":"gif","c":"word/media/image133.png"})
.
当![](https://wkrtcs.bdimg.com/rtcs/image?w=59&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"59","h":"19","dataType":"gif","c":"word/media/image145.png"})
时，，直线过定点与已知矛盾；
当![](https://wkrtcs.bdimg.com/rtcs/image?w=63&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"63","h":"41","dataType":"gif","c":"word/media/image148.png"})
时，，直线过定点.
综上可知，直线![](https://wkrtcs.bdimg.com/rtcs/image?w=9&md5sum=1174e6ab6a0cb00e5bf9540d1b1d0b3c&sign=15b34dd0f2&rtcs_flag=1&rtcs_ver=3.2&l=webapp&bucketNum=86&ipr={"t":"img","w":"9","h":"19","dataType":"gif","c":"word/media/image151.png"})
过定点.…………………………………………12分
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