a,
$\Delta$ AHB, BI phân giác.
$\Rightarrow \frac{AB}{BH}=\frac{AI}{IH}$
$\Leftrightarrow AB.IH= BH.AI$
b, (sửa thành $AH^2=BH.HC$)
$\Delta$ AHB và $\Delta$ CHA có:
$\widehat{AHB}=\widehat{CAB}=90^o$
$\widehat{BAH}=\widehat{HCA}=90^o-\widehat{HAC}$
$\Rightarrow \Delta$ AHB $\backsim$ $\Delta$ CHA (g.g)
$\Rightarrow \frac{AH}{BH}=\frac{HC}{AH}$
$\Leftrightarrow AH^2=BH.CH$
c, (chưa rõ đề)