输血狗狗第107题讨论～～～～～大神来~~

sdcar2010

For ease of calculation, let's rotate the figure a bit so that both  the point O (center of the circle) and the point P are on the y-axis.

Q (x, y) is on the left side of the circle. Therefore, x^2 + y^2 = 5; wherein x is between 0 and -5; y is between 5 and -5 (on the left side of the circle).
The distance (D) between P and Q is the square root of [x^2 + (13-y)^2]. To find the maximum value for this value D, we just need to find the maximum value for  [x^2 + (13-y)^2].
[x^2 + (13-y)^2] = x^2 + 13^2 - 26y + y^2 = 169 + (x^2 + y^2) - 26y = 169 + 25 - 26y

Apparently the value of D depends the value of y. So the minimum of D is when y = 5; and the maximum of D is when y = -5.

Back to the REAL question, the answer is similar if you know a bit of symmetry and logic. The maximum of PQ will be reached when Q is at the lowest, possible value of y.

Monkey43

我不理解为什么会是12<x<18呢，我觉得就是8<x<18....

Monkey43

求指导啊，还是不明白为什么最小是和A点重合？

有竹无心

A good picture is more than a thousand words . . .

PQ1 (Blue) is the shortest length.

PQ2 (Red) is the longest length.

End of story.

-- by 会员 sdcar2010 (2011/7/10 11:21:18)

i think this one is right.

gmat6276

不理解讨论稿里为什么说最小值是12，求解！！！！！！！！不是8吗？就算有在左半圆的这个条件？

rainbowmanutd

不理解讨论稿里为什么说最小值是12，求解！！！！！！！！不是8吗？就算有在左半圆的这个条件？

-- by 会员 gmat6276 (2011/7/12 16:32:26)

i think it's 8

sdcar2010

It all depends on the relative position of PQ and the "left half" of the circle.

pig贝贝

PA=12，那Q到圆的距离，就算是左半边，肯定还是有小于12的，比如图里的Q1点，就可以推翻楼主的结论了，开始我不知道怎么算的也是12和18之间，可是后来就画不出来那个情况了，LZ能否贴个12的图上来呢

shadowcynthia

求楼主给个12 的..... 只能理解到8 悲催...

sdcar2010

Here is the graph. The shortest is 12 and the longest is 18.