Câu 1 như hình.
Câu 4:
a,
$\Delta$ HBA và $\Delta$ ABC có:
$\widehat{AHB}=\widehat{CAB}=90^o$
$\widehat{C}$ chung
$\Rightarrow \Delta$ HBA $\backsim$ $\Delta$ ABC (g.g) (*)
b,
$AC=\sqrt{BC^2-AB^2}=8cm$
(*) $\Rightarrow \frac{AH}{AB}=\frac{AC}{BC}$
$\Leftrightarrow AH=\frac{6.8}{10}=4,8cm$
$\Rightarrow BH=\sqrt{AB^2-AH^2}=3,6cm$
c,
$\Delta$ AIH và $\Delta$ AHB có:
$\widehat{BAH}$ chung
$\widehat{AIH}=\widehat{AHB}=90^o$
$\Rightarrow \Delta$ AIH $\backsim$ $\Delta$ AHB (g.g)
$\Rightarrow \frac{AI}{AH}=\frac{AH}{AB}$
$\Leftrightarrow AH^2=AI.AB$ (1)
Tương tự, $\Delta$ AKH $\backsim$ $\Delta$ AHC (g.g)
$\Rightarrow AH^2=AK.AC$ (2)
(1)(2) $\Rightarrow AI.AB=AK.AC$
d,
$\Delta$ ADB, DE phân giác
$\Rightarrow \frac{AE}{EB}=\frac{DA}{DB}$
$\Delta$ ADC, DF phân giác
$\Rightarrow \frac{CF}{AC}=\frac{DC}{DA}$
$\Rightarrow \frac{AE}{EB}.\frac{DB}{DC}.\frac{FC}{FA}=\frac{DA}{DB}.\frac{DB}{DC}.\frac{DC}{DA}=1$
