Giải thích các bước giải:
a.Ta có $AH\perp BC\to AH^2=AB^2-BH^2=AC^2-CH^2$
$\to AB^2+CH^2=AC^2+BH^2$
b1.Ta có:
$M$ là trung điểm $BC\to MB=MC$
Ta có:
$BH=MB-HM=\dfrac12BC-HM$
$CH=MC+HM=\dfrac12BC+HM$
$\to BH^2+CH^2=\left(\dfrac12BC-HM\right)^2+\left(\dfrac12BC+HM\right)^2$
$\to BH^2+CH^2=\dfrac12BC^2+2HM^2$
$\to BH^2+AH^2+CH^2+AH^2=\dfrac12BC^2+2\left(AH^2+HM^2\right)$
$\to AB^2+AC^2=\dfrac12BC^2+2AM^2$
b2.Ta có:
$AB^2+CH^2=AC^2+BH^2$
$\begin{split}\to AB^2-AC^2&=BH^2-CH^2\\&=\left(BH-CH\right)\left(BH+CH\right)\\&=\left(\left(\dfrac12BC-HM\right)-\left(\dfrac12BC+HM\right)\right)\cdot BC\end{split}$
$\to AB^2-AC^2=-2HM\cdot BC$
$\to AC^2-AB^2=2BC.HM$
