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The diagonal $BD$ of parallelogram $ABCD$ is divided by segment $AE$ in the ratio $1:2$. If $BE = 1.8\text{ cm}$, find the length of $AD$.
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Solution: Proving $\Delta OAD \sim \Delta OEB$ (By AA similarity criterion)
Therefore $\frac{OB}{OD} = \frac{EB}{AD} \Rightarrow \frac{1}{2} = \frac{1.8}{AD}$
$\Rightarrow AD = 3.6\text{ cm}$
Therefore $\frac{OB}{OD} = \frac{EB}{AD} \Rightarrow \frac{1}{2} = \frac{1.8}{AD}$
$\Rightarrow AD = 3.6\text{ cm}$