$\text{Ta có: BC = HB + HC = 2 + 8 = 10 (cm)}$
$\text{Áp dụng định lý Py - ta - go cho ΔABC, ta có:}$
$AB^{2}$ $\text{+}$ $AC^{2}$ $\text{=}$ $BC^{2}$
`Hay:` $AB^{2}$ $\text{+}$ $AC^{2}$ $\text{=}$ $10^{2}$
`->` $AB^{2}$ $\text{+}$ $AC^{2}$ $\text{=}$ `100`
$\text{Áp dụng định lý Py - ta - go cho ΔAHC, ta có:}$
$AH^{2}$ $\text{+}$ $CH^{2}$ $\text{=}$ $AC^{2}$
`Hay:` $AH^{2}$ $\text{+}$ $8^{2}$ $\text{=}$ $AC^{2}$
`->` $AH^{2}$ $\text{+ 64}$ $\text{=}$ $AC^{2}$
$\text{Áp dụng định lí Py - ta - go cho ΔAHB, ta có: }$
$AH^{2}$ $\text{+}$ $BH^{2}$ $\text{=}$ $AB^{2}$
`Hay:` $AH^{2}$ $\text{+}$ $2^{2}$ $\text{=}$ $AB^{2}$
`->` $AH^{2}$ $\text{+ 4}$ $\text{=}$ $AB^{2}$
$\text{Lại có: }$
$AB^{2}$ `+` $AC^{2}$ `=` $AH^{2}$ $\text{+}$ $CH^{2}$ `+` $AH^{2}$ $\text{+}$ $BH^{2}$
`->` $AB^{2}$ `+` $AC^{2}$ `=` $AH^{2}$ $\text{+}$ `64` `+` $AH^{2}$ $\text{+}$ `4`
`->` `100` `=` $2(AH^{2})$ `+` `64` `+` `4`
`->` `100` `=` $2(AH^{2})$ `+` `68`
`->` $2(AH^{2})$ `=` `100` `-` `68`
`->` $2(AH^{2})$ `=` `32`
`->`$AH^{2}$ $\text{= 32 : 2 = 16}$
`->` `AH` `=` $\sqrt[]{16}$ `=` `4`
$\text{Vậy AH = 4 cm}$
`_`$\color{darkred}{Selina}$`_`
