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因為 B、C、D 三點共線，所以 [∠BCA + ∠ACE + ∠ECD = 180°]，而，[∠BCA = 60°] 且，[∠ECD = 60°]，[∠ACE = 60°]，用相似三角形的性質來解 [EF] 的長度。
* [∠BCF = ∠ECF = 60°]
* [∠CBF = ∠CEF] (因為 [∠ABC = ∠DCE = 60°]，且 B, C, D 共線)
* [△BCF ∽ △ECF] (AA 相似)
因為 [△ABC] 是正三角形，所以 [AC = BC = 3]。
* [CF = AC - AF = 3 - AF]
[EF = x]，用相似三角形的比例關係
* [BC/CE = CF/EF]
* [3/6 = (3 - AF)/x]
* [1/2 = (3 - AF)/x]
* [x = 2(3 - AF)]
* [∠AFB = ∠CFE] (對頂角)
* [∠ABF = ∠CEF] (內錯角)
* [△ABF ∽ △CEF] (AA 相似)
* [AB/CE = AF/CF]
* [3/6 = AF/(3-AF)]
* [1/2 = AF/(3-AF)]
* [3 - AF = 2AF]
* [3AF = 3]
* [AF = 1]
* [EF = x = 2(3 - AF) = 2(3 - 1) = 2 * 2 = 4]
希望這樣你能懂👍
[答案]
[EF = 4]
麻煩了