\[\begin{array}{l}
a)\,\,\,CM:\,\,AO \bot BC\\
AB,\,\,\,AC\,\,\,la\,\,\,2\,\,tiep\,\,tuyen\,\,cat\,\,nhau\\
\Rightarrow AB = AC\\
\Rightarrow A\,\,thuoc\,\,duong\,\,\,trung\,\,truc\,\,cua\,\,BC.\\
Lai\,\,co:\,\,\,OB = OC = R\\
\Rightarrow O\,\,thuoc\,\,duong\,\,\,trung\,\,truc\,\,cua\,\,BC.\\
\Rightarrow AO \bot BC\,\,\left( {dpcm} \right).\\
b)\,\,Ta\,co:\,\,\angle BCD\,\,\,la\,\,\,goc\,\,noi\,\,tiep\,\,chan\,\,nua\,\,duong\,\,tron\\
\Rightarrow \angle BCD = {90^0}\,\,\,hay\,\,BC \bot CD.\\
Lai\,\,\,co:\,\,\,BC \bot AO\,\,\left( {cmt} \right)\\
\Rightarrow CD//AO\,\,\,\,\left( {dpcm} \right).\\
c)\,\,\,Ta\,\,\,co:\,\,\,AB = \sqrt {O{A^2} - O{B^2}} = \sqrt {{5^2} - {3^2}} = 4.\\
\Rightarrow BH = \frac{{BO.BA}}{{OA}} = \frac{{3.4}}{5} = 2,4.\,\,\left( {BH \bot OA = \left\{ H \right\}} \right).\\
\Rightarrow {S_{ABC}} = \frac{1}{2}BH.OA = \frac{1}{2}.2,4.5 = 6\,\,c{m^2}.\\
Ta\,\,co:\,\,\,BH \bot OA = \left\{ H \right\}\\
\Rightarrow H\,\,la\,\,trung\,\,diem\,\,cua\,\,BC.\\
\Rightarrow BC = 2BH = 2.2,4 = 4,8.\\
\Rightarrow {C_{ABC}} = AB + AC + BC = 4 + 4 + 4,8 = 12,8.
\end{array}\]
