Question
Id trapezium ABCD (adjoining figure), side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then find OD.
✓
Answer
$\begin{array}{l}\text { In } \triangle AOB \text { and } \triangle COD \\ \Rightarrow \angle AOB \angle COD \text { (opposite angles) } \\ \Rightarrow \angle CDO \cong \angle ABO \text { (Alternate angles } \because AB \| DC ) \\ \Rightarrow \triangle AOB \sim \triangle COD \text { (By AA Test) } \\ \Rightarrow \frac{ AB }{ DC }=\frac{ OB }{ OD } \text { (corresponding sides are proportional) } \\ \Rightarrow OD =\frac{ OB \times DC }{ AB } \\ \Rightarrow OD =\frac{15 \times 6}{20} \\ \Rightarrow OD =4.5\end{array}$
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