Question

In figure, `\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}` and AB = 5 cm. Find the value of DC.

Answer 1

In ∆AOB and ∆COD, we have

∆AOB = ∆COD [Vertically opposite angles]

`\frac{AO}{OC}=\frac{BO}{OD} `

So, by SAS-criterion of similarity, we have

∆AOB ~ ∆COD

`\Rightarrow \frac{AO}{OC}=\frac{BO}{OD}=\frac{AB}{DC}`

`\Rightarrow \frac{1}{2}=\frac{5}{DC} [∵ AB = 5 cm]`

⇒ DC = 10 cm