a) $\triangle OBM=\triangle OAM$ (c.c.c) $\Rightarrow \widehat{OBM}=\widehat{OAM}=90^{\circ}\Rightarrow$ đpcm.
b) $BH=AH=\dfrac{AB}2=12 (cm)\Rightarrow OH=\sqrt{OB^2-BH^2}=9 (cm)$
$\triangle OBM$ vuông tại $B, BH\perp OM\Rightarrow OB^2=OH.OM\Rightarrow OM=\dfrac{OB^2}{OH}=25 (cm)$