1)在圖中，M是AB上的一點使OM丄AB，E是CR上的一點使CE=ED。已知ED=AB，AM=3cm及OE=4.5cm，求
(a)圓的半徑OD;
(b)OM的長度，準確至一位小數。
圖片參考：http://imgcld.yimg.com/8/n/HA07267368/o/701103120078113873389170.jpg
F.4 圓的基本性質 1題
2011-03-13 12:14 am
回答 (2)
2011-03-13 12:48 am
✔ 最佳答案
(a)OM丄AB (已知)BM = AM = 3 cm (圓心至弦的垂線平分弦 )DE = BM + AM = 3+3 = 6cmCE=EDOE丄CD (圓心至弦中點的連線垂直於弦 )在 △OED 中OE^2 + ED^2 = OD^2 (畢氏定理)4.5^2 + 6^2 = OD^2OD^2 = 56.25 ∴ OD = 7.5cm(b)OA = OD = 7.5cm (半徑)在 △OMA中OM^2 +MA^2＝OA ^2 (畢氏定理)OM^2 =７。５^2－３^2＝ ４７。２５∴ OM＝ ６。９cm
2011-03-13 2:49 am
(a) AB = 2AM = 6 cm
DE = AB = 6 cm
OD^2 = DE^2 + CE^2 = 36 + 20.25 = 56.25
OD = 7.5 cm
(b) OM^2 = OA^2 - AM^2 = 56.25 - 9 = 47.25
OM = 6.9 cm (準確至一位小數)
DE = AB = 6 cm
OD^2 = DE^2 + CE^2 = 36 + 20.25 = 56.25
OD = 7.5 cm
(b) OM^2 = OA^2 - AM^2 = 56.25 - 9 = 47.25
OM = 6.9 cm (準確至一位小數)
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