[tex]AB||CD\Longrightarrow \Delta AOB \sim \Delta COD\\\\
\frac{AO}{OC} = \frac{OB}{OD} = \frac{AB}{CD}\\\\
\frac{AO}{OC} = \frac{48}{30}= \frac{8}{5}\\\\
AO+ \frac{OC}{OC}=8+ \frac{5}{5} \\\\
\frac{AC}{OC}= \frac{13}{5} \Longrightarrow \frac{52}{OC}= \frac{13}{5}\Longrightarrow OC= \frac{52*5}{13}\Longrightarrow \bold{OC=20~cm} \\\\[/tex]
[tex]\Longrightarrow
AO=52-20 \Longrightarrow \bold{AO=32 ~cm} \\\\
\frac{OB}{OD} = \frac{48}{30}= \frac{8}{5}\\\\
OB+\frac{OD}{OD} =8+ \frac{5}{5}\\\\
\frac{BO}{OD}= \frac{13}{5}\\\\
\frac{65}{OD} = \frac{13}{5} \Longrightarrow OD= \frac{65*5}{13}\Longrightarrow \bold{OD=25~cm}\Longrightarrow OB=65-25\\\\\Longrightarrow \bold{OB=40~cm}[/tex]
