Giải thích các bước giải:
a.Xét $\Delta AHB,\Delta ABC$ có:
Chung $\hat B$
$\widehat{AHB}=\widehat{BAC}=90^o$
$\to \Delta AHB\sim\Delta CAB(g.g)$
$\to \dfrac{AH}{CA}=\dfrac{AB}{BC}=\dfrac35$
$\to AH=\dfrac35AC= 12$
b.Xét $\Delta AHP,\Delta HAC$ có:
Chung $\hat A$
$\widehat{APH}=\widehat{AHC}(=90^o)$
$\to\Delta AHP\sim\Delta ACH(g.g)$
$\to \dfrac{AH}{AC}=\dfrac{AP}{AH}$
$\to AH^2=AP.AC$
c.Tương tự câu b $\to AH^2=AQ.AB$
$\to AQ.AB=AP.AC$
$\to \dfrac{AP}{AC}=\dfrac{AP}{AB}$
Mà $\widehat{PAQ}=\widehat{BAC}$
$\to\Delta APQ\sim\Delta ABC(c.g.c)$
