Question

Diagonals AC and BD of a trapezium ABCD with $AB\parallel DC$ intersect each other at the point O ,$\frac{OA}{OC}=?$

• A. $\frac{BD}{OB}$
• B. $\frac{BO}{OD}$
• C. $\frac{AO}{OB}$
• D. $\frac{CO}{OD}$

Answer 1

Answer: (B)

$\frac{BO}{OD}$

In $△AOB$ and $△COD$,

$\angle AOB=\angle COD$ ....Vertically opposite angles

$\angle OAB=\angle OCD$ ...Alternate angles since $AB\parallel CD$

$\therefore △AOB\sim △COD$ ....A.A test of similarity

$\therefore \frac{OA}{OC}=\frac{OB}{OD}=\frac{AB}{CD}$ ...C.S.S.T.