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In the given figure, $\frac{AO}{OC} = \frac{BO}{OD} = \frac{1}{2}$ and AB = $5$ cm. Find the length of DC.
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Sol. In $\triangle AOB$ and $\triangle COD$
$\frac{AO}{OC} = \frac{BO}{OD}$ (Given)
$\angle AOB = \angle COD$ (V.O.A.)
$\therefore \triangle AOB \sim \triangle COD$ (SAS rule) (1 Mark)
$\frac{AO}{OC} = \frac{AB}{CD}$ (C.P.S.T.)
$\frac{1}{2} = \frac{5}{CD}$
$\Rightarrow CD = 10$ cm (1 Mark)
$\frac{AO}{OC} = \frac{BO}{OD}$ (Given)
$\angle AOB = \angle COD$ (V.O.A.)
$\therefore \triangle AOB \sim \triangle COD$ (SAS rule) (1 Mark)
$\frac{AO}{OC} = \frac{AB}{CD}$ (C.P.S.T.)
$\frac{1}{2} = \frac{5}{CD}$
$\Rightarrow CD = 10$ cm (1 Mark)