Question

In the trapezium PQRS, PQ is parallel to RS and the diagonals intersect at O. If $OP.SR=m(OR.PQ)$, then the value of m is :

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $1$

In Trapezium PQRS, $\Delta OPQ$ is similar to $\Delta OSR$ by AA similarity.
$\therefore \frac{OP}{OR}=\frac{OS}{OQ}=\frac{PQ}{SR}$
$\therefore OP.SR=OR.PQ$
Hence, $m=1$