a,[tex]\widehat{BB'C}=\widehat{CC'B}=90^{\circ}=>BC'B'C nội tiếp
b,[tex]\widehat{ABC}=\frac{1}{2}sd\overbrace{AC}=\frac{1}{2}(sd\overbrace{CM}+\overbrace{AM}) =\widehat{CAM}+\widehat{ANM}; \widehat{AB'C'}=\widehat{CAM}+\widehat{AMN}; \widehat{ABC}=\widehat{ABC}=>\widehat{ANM}=\widehat{AMN}=>AM=AN[/tex]
c,[tex]\widehat{ANM}=\widehat{ACM}=>\Delta AMB'\sim \Delta ACM=>AM^2=AB'*AC[/tex]
[tex]\Delta AB'C'\sim \Delta ABC=>AB'*AC=AC'*AB=>AM^2=AC'*AB[/tex][/tex]