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