Question

In trapezium ABCD, side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then Find OD.

Answer 1

Given:
side AB || side DC
AB = 20,
DC = 6,
OB = 15
In △COD and △AOB
∠COD = ∠AOB (Vertically opposite angles)
∠CDO= ∠ABO (Alternate angles, CD ||BA and BD is a transversal line)
By AA test of similarity
△COD ∼ △AOB
$$\begin{gathered} \therefore \frac{\mathrm{CD}}{\mathrm{AB}}=\frac{{\displaystyle \mathrm{OD}}}{{\displaystyle \mathrm{OB}}}\left(\mathrm{Corresponding}\mathrm{sides}\mathrm{are}\mathrm{proportional}\right) \\ \Rightarrow \frac{6}{20}=\frac{\mathrm{OD}}{15} \\ \Rightarrow \mathrm{OD}=4.5 \end{gathered}$$