Prep T1-PS

[dianechiu]

In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arcABC is 24, whatis the approximate diameter of the circle?
(A)5 (B)8 (C)11 (D)15 (E)19
ans:C

在寫的時候思路是
arcABC=1/3圓周長
圓周=24*3=72=直徑*拍
直徑=72/拍=23...根本沒這個答案

想請教大家這題該怎麼做?謝謝

[zacchen]

[quote="dianechiu"]In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arcABC is 24, whatis the approximate diameter of the circle?
(A)5 (B)8 (C)11 (D)15 (E)19
ans:C

在寫的時候思路是
arcABC=1/3圓周長
圓周=24*3=72=直徑*拍
直徑=72/拍=23...根本沒這個答案

想請教大家這題該怎麼做?謝謝 :laugh[/quote]
arcABC 應該是大約2/3圓周長,1/3 太少了
所以應該是2rpai=24/(2/3)
2r=36/pai
2r=11.46
Answer:C

[nemolee]

In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arcABC is 24, whatis the approximate diameter of the circle?
(A)5 (B)8 (C)11 (D)15 (E)19
ans:C

在寫的時候思路是
arcABC=1/3圓周長
圓周=24*3=72=直徑*拍
直徑=72/拍=23...根本沒這個答案

想請教大家這題該怎麼做?謝謝

arcABC 應該是大約2/3圓周長,1/3 太少了
所以應該是2rpai=24/(2/3)
2r=36/pai
2r=11.46
Answer:C

弱弱的問一下..
arc ABC 應該是大約 2/3 圓周長.......是大約怎麼求出來ㄉ?
2r拍 = 24 / (2/3) ==> why 24 / (2/3)

我利用 圓周 = 拍d = 拍2r = 24, 怎麼算都是大約是 d = 8 這個答案..

請各位指教.... 謝~

[nemolee]

自己來ding一下... 請路過好心ㄉ人來幫幫忙... 謝謝

[Huang Hsin-Yi]

arc AB=arc BC= arc AC 因為正三角形各角60度對應的arc相等
又arc ABC= arc AB+arc BC=2/3 圓周=24

therefore 圓周=36
圓周=2*拍*r=36 --->r=5.6--->d=11.3