Question

In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

• A. $OB=\frac{1}{2}BD$
• B. $AP=\frac{1}{2}BC$
• C. $PD=AP$
• D. $OA=\frac{1}{2}CD$

Answer 1

The correct option is A $OB=\frac{1}{2}BD$

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

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