数学题啊~~~~~sos

chriswendy35

a certain area has its center at point p and has radius 4, and point x and y lie in the same plane as the circular area. does point y lie outside the circul area?
(1)the distance between p and x is 4.5
(2)the distance between x and y is 9

我的理解是只要XY>9,且X在圆上，那么Y必然不在圆上，因为圆上最大距离，即圆的直径为8。
可是答案是C，迷惑了
猜测是不是lie in the same plane as the circular area没能理解，请高手指教

zongzeng90

same plane 是指在一个平面内 楼主想多了  就是把圆和两个点定在一个平面内 防止你考虑空间几何的可能性

chriswendy35

题目问你Y是不是在圆的外面？那么y在圆的里面和外面都成立。

(1)不能得出y的位置，只能知道x在圆外。
( ...
banglixing 发表于 2010-8-18 06:32

    “point x and y lie in the same plane as the circular area.”
是不是说X,Y 相对于圆对称？如果对称的话，X不在圆，XY距离又大于了最大直径8，那么y就不在圆上了啊？

banglixing

题目问你Y是不是在圆的外面？那么y在圆的里面和外面都成立。

(1)不能得出y的位置，只能知道x在圆外。
(2)单独不成立，因为你不知道x的位置，所以更无法知道y的位置。

二者结合可知y不在圆内。

bettytons

1) insufficient b/c it gives us no information on point Y.
2) insufficient b/c it gives us no information on whether any of the two points are located inside or outside the circle.

together:

we know point x is outside the circle, (distance of 0.5 away from the point ON the circle).

xy = 9

the diameter of the circle is 8, which means the largest distance covered and the point y can still be covered inside the circle is 8.

4.5 + 4 = 8.5 (can be the maximum distance allowed for xy for y to still be a part inside the circle).

Therefore point y will lie outside the circle.