Giải thích các bước giải:

a.Xét $$\Delta AHB,\Delta ABC$$ có:

Chung $$\hat B$$

$$\widehat{AHB}=\widehat{BAC}(=90^o)$$

$$\to \Delta BAH\sim\Delta BCA(g.g)$$

$$\to \dfrac{BA}{BC}=\dfrac{BH}{BA}$$

$$\to BA^2=BH\cdot BC$$

b.Xét $$\Delta ACK,\Delta ABM$$ có:

$$\widehat{ACK}=90^o-\widehat{ACB}=\widehat{ABC}=\widehat{ABM}$$

$$\widehat{KAC}=90^o-\widehat{CAM}=\widehat{MAB}$$

$$\to \Delta ACK\sim\Delta ABM(g.g)$$

c.Gọi $$AI\cap BC=D$$

Xét $$\Delta DAM,\Delta DCI$$ có:

Chung $$\hat D$$

$$\widehat{DMA}=\widehat{AMB}=\widehat{AKC}=\widehat{DKC}$$

$$\to\Delta DAM\sim\Delta DCK(g.g)$$

$$\to \dfrac{DA}{DC}=\dfrac{DM}{DK}$$

Mà $$\widehat{KDM}=\widehat{ADC}$$

$$\to \Delta DMK\sim\Delta DAC(c.g.c)$$

$$\to \widehat{DKM}=\widehat{ACD}$$

$$\to \widehat{AKM}=\widehat{ACB}$$

Mà $$\widehat{KAM}=\widehat{CAB}(=90^o)$$

$$\to \Delta AMK\sim\Delta ABC(g.g)$$