格式练习：一道数学题以及解题过程。

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如图，AB是\odot O的直径，点C、D在\odot O上，CE\bot AB，DF\bot AB，垂足分别为E、F，且AE=BF，求证：\overset{\frown}{AC}=\overset{\frown}{BD}.

证明：

连接OC,\,\, OD.

由题知，OC=OD=OA=OB.

又\because AE=BF,\,CE\bot AB,\,DF\bot AB

\therefore OE=OF,\,\angle CEO=\angle DFO=90^{\circ}.

\therefore CE\parallel DF.

在\mathrm{Rt}\triangle ECO与\mathrm{Rt}\triangle FDO中

\begin{cases} OC=OD \\ OE=OF \end{cases}

\therefore \mathrm{Rt}\triangle ECO \cong \mathrm{Rt}\triangle FDO.\left(H\!L\right)

\therefore \angle EOC=\angle FOD.

\therefore \angle AOC=\angle BOD.

\therefore \overset{\frown}{AC}=\overset{\frown}{BD}.

Lake桑

2019.1.5


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