题目
题型:解答题难度:困难来源:福建省模拟题
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020955-66039.gif)
(1)直接填空:AP=________cm,AQ=_________cm(用含t的代数式表示,其中0<t<5);
(2)若点Q关于菱形ABCD的对角线交点O的对称点为M,过点P且垂直于AB的直线l交菱形ABCD的边AD(或CD)于点N。
①当t为何值时,PM+MN的值最小?
②当t为何值时,△PQM的面积S有最大值,此时最大值是多少?
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020955-18206.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020955-52791.gif)
如图,在
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020955-80794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020956-15302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020956-77290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020956-62553.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020956-60894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020956-32372.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020957-26576.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020957-63224.gif)
②如图1,若
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020957-14139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020957-82745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020957-12378.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020958-24456.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020958-77694.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020958-45729.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020958-64954.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020958-21875.gif)
∴△APQ∽△ABO,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020959-69600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020959-44214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020959-85665.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020959-29911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020959-56933.gif)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021000-36980.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021000-62769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021000-85170.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021000-44075.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021000-85219.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021001-21089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021001-22693.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021001-51258.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021001-29295.gif)
∴△QCP∽△OCB,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-65484.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-32053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-34598.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-42774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-84606.gif)
综上,当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021002-85492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021003-65147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021003-11183.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021003-48716.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817021003-69286.gif)
核心考点
试题【如图,菱形ABCD的边长为20cm,∠ABC=120°、动点P、Q同时从点A出发,其中点P以4cm/s的速度,沿A→B→C的路线向点C运动;点Q以的速度,沿A→】;主要考察你对列代数式等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817020953-44001.gif)
(2)第二幅邮票比第一幅邮票的面积大多少?
最新试题
- 1下列计算中,正确的是( )A.+=B.×=6C.÷=4D.-=
- 2The results of the medical checkup suggested that my father
- 3根据汉语提示完成句子1. Someone tried to (毒死我们的狗). 2. The article
- 4将一袋桔子分给若干个儿童,如果每人分4个桔子,则剩下9个桔子;如果每人分6 个桔子,则最后一个儿童分得的桔子数将少于3个
- 5The Internet, as well as news paper and magazines, an
- 6请在以下两个题中任选一题作文。(1)我心中的那 (一轮太阳、一抹绿
- 7(本题满分14分)本题共有2个小题,第1小题满分7分,第2小题满分7分.(理科)已知四棱锥的底面是直角梯形,,,侧面为正
- 8唐太宗时期,假设国家要在关中一带修建一项大型水利工程,这项工程的实施按制度规定其运作程序是 [ ]A、尚书省→
- 9有“塞上江南”之称的是[ ]A.宁夏平原 B.河套平原 C.华北平原D.东北平原
- 10作文:(50分)自信,就是相信自己。自信的人,能正确对待自己,能以积极的态度对待生活,坚信自己能取得成功。自信的表现多种
热门考点
- 1对于“H2O→O2”和“O2→H2O”这两个过程的分析不正确的是[ ]A.前者可表示为光合作用的光反应阶段B.前
- 2已知a=a-2,b=(3-1)0,c=(-1)3,则a、b、c的大小关系是( )A.a>b>cB.b=a>cC.c>a
- 3(8分)在编号为A、B、C、D的四支试管中分别盛有NaHSO4、NaHCO3、BaCl2、BaCO3固体,在只有蒸馏水和
- 4下列选用的相关仪器符合实验要求的是[ ]A.存放浓硝酸 B.分离水和乙酸乙酯 C.准确量取9.50mL水 D.实
- 5 红底黑字,稳重而鲜艳的春联增添了新春的喜庆。春联要求上下联要字数相等,断句一致;平仄相合,音调和谐;要词性相对,位置相
- 6已知:如图AD为△ABC的高,E为AC上一点,BE交AD于F,且有BF=AC,FD=CD,求证:BE⊥AC.
- 7开展社会调查活动是同学们了解社会、扩大知识视野、培养科学素养的社会实践活动,为完成下列调查内容而选择的对象或渠道,其不合
- 8如果等差数列{an}的前n项的和Sn=12n2-n,那么a7=______.
- 9 Our English teacher is often _______ to give a talk on Engl
- 10已知:函数f(x)=x2-bx+c,若f(1-x)=f(1+x),且f(0)=3,(1)求:b、c的值;(2)试比较f(