\(\begin{array}{l}
a)\,\,\,Vi\,\,Oz\,\,la\,\,\,tia\,\,phan\,\,giac\,\,cua\,\,\,\angle xOy\\
\Rightarrow \angle xOz = \angle zOy\\
hay\,\,\angle AOH = \angle HOB\\
Xet\,\,\Delta AOH\,\,\,va\,\,\Delta BOH\,\,\,ta\,\,co:\\
\angle AOH = \angle HOB\,\,\left( {cmt} \right)\\
OH\,\,chung\\
\angle OHA + \angle OHB = {90^0}\\
\Rightarrow \,\Delta AOH\,\, = \,\,\Delta BOH\,\,\,\left( {g - c - g} \right)\\
\Rightarrow OA = OB\,\,\,\left( {dpcm} \right).\\
b)\,\,\,Ta\,\,co:\,\,\,AC//Oy\\
\Rightarrow \angle CAH = \angle ABO\,\,\,\left( {2\,\,goc\,\,so\,\,le\,\,trong} \right)\\
ma\,\,\,\angle OAH = \angle HBO\,\,\,\left( {do\,\,\Delta AOH\,\, = \,\,\Delta BOH} \right)\\
\Rightarrow \angle CAH = \angle OAH\,\,\left( { = \angle HBO} \right)\\
Xet\,\,\Delta AOH\,\,\,va\,\,\Delta ACH\,\,\,ta\,\,co:\\
\angle CAH = \angle OAH\,\,\,\left( {cmt} \right)\\
AH\,\,chung\\
\angle OHA + \angle OHC = {90^0}\\
\Rightarrow \,\Delta AOH\,\, = \,\,\Delta ACH\,\,\,\left( {g - c - g} \right)\\
\Rightarrow OA = OC\,\,\,\,\left( {dpcm} \right).
\end{array}\)
