一条弧所对的圆心角为135°，弧长等于半径为5cm的圆的周长的3倍，则这条弧的半径为____ 。

____

已知：如图，△ABC中， AD是角平分线．

求证： $\frac{AB}{AC}=\frac{BD}{DC}$ ．

证明：过C作CE∥DA，交BA的延长线于E．

∴ $\angle 1=\angle E,\angle 2=\angle 3$ ． ①

$\because$  AD是角平分线，

∴ $\angle 1=\angle 2$ ．

$\therefore$ $\angle 3=\angle E$ ．

$\therefore AC=AE$ ．      ②

又 $\because AD//CE$ ，

$\therefore \frac{AB}{AE}=\frac{BD}{DC}$ ．       ③

$\therefore$ $\frac{AB}{AC}=\frac{BD}{DC}$ ．

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