Question

In the given figure, $P$ is the mid point of side $CD$ and one of the vertices of parallelogram $ABCP.$ Which of the following options is correct?

• A. OA = CD
• B. PD = AP
• C. AP = BC
• D. OB = BD

Answer 1

The correct option is D

OB = BD

$ABCP$ is a parallelogram with $OP\parallel BC$
Since, $P$ is the mid point of $CD$ and $OP\parallel BC,O$ is the mid point of $BD$ by converse of mid point theorem.

Therefore, $OB=\frac{1}{2}BD$