Question

If PQRS is a parallelogram inscribed in a circle then it is a

• A. Rhombus
• B. Square
• C. Rectangle
• D. Trapezium

Answer 1

The correct option is C Rectangle

If PQRS is a parallelogram then if it is inscribed in a circle.

Ref. image

$PQ||RS$

$QR||PS$

$\Rightarrow$In $\Delta POS$ & $\Delta QOR$

$\Rightarrow$$OP=OQ$ (radii)

$\Rightarrow$$\angle POS=\angle QOR$ (vertically opposite angles)

$\Rightarrow$$OR=OS$ (Radii)

$\Rightarrow$$\Delta POS\cong \Delta QOR$

then $PS=QR$

$\Rightarrow$similarly from $\Delta POQ$ and $\Delta ROS$

$\Rightarrow$$PQ=RS$

$\Rightarrow$$PQRS$ is a rectangle