GWD11-Q2

[jhchiou]

Q2: In the figure, point A,B,C,D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle , and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB=3 and BC=2
(2) CD=1 and DE=4

我看到不同版本的答案, 可否幫忙告訴我正確ans, Tks!

[liwuu]

印象中這一題的正確答案為D!!

[stupidgirl]

應該是D~條件1與2都可得大圓與小圓的半徑~然後算出面積^^

[jhchiou]

謝謝!
我當初也是求出D, 但是有看到其他的答案像A....
害我覺得怪怪的????

[stupidgirl]

我記得原來答案是A~後來有更正成D^^

[michelle610]

為什麼B可以ㄚ 我還是看不出來B要怎麼求出小圓ㄉ半徑ㄟ 請好心人告ㄓㄧ下 謝謝

[michelle610]

哈哈 別理我 我知道哪裡對了

[evelyn]

對不起 我還是不知道為什麼(2)對呀 請指點 謝謝

[hsiaoj]

對不起 我還是不知道為什麼(2)對呀 請指點 謝謝

這題有圖片 , 五點排序為
A B C D E
(SORRY 沒有圖, 請自行參考gwd)

(2) CD =1 and DE = 4

CE=CD+DE=5 (大圓半徑)
AE=5*2=10 (大圓直徑)
AD=AE-DE=10-4=6 (小圓直徑) , 小圓半徑=6/2=3
有兩個圓的半徑即可得到所求

[huiz]

圖補上

[chris8888]

為了方便圖文對照, 我再貼一次題目
Q2: In the figure, point A,B,C,D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle , and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB=3 and BC=2
(2) CD=1 and DE=4

(1). 要算大圓面積減掉小圓面積, 很簡單就是算出各自的半徑即可
segment AB 是小圓的radius, AB+BC是大圓的Radius 可解

(2). 大圓的Radius是CD+DE=5, AB + BC(大圓半徑左邊) = CD + DE(大圓半徑右邊)
AB+BC+CD=2CD + DE (設AB=r) (另外BC+CD = r)(這裡有一點技巧兩邊加上CD)
r + r = 1+5
2r = 6
r = 3