Question

Any cyclic parallelogram is a ______.

• A. rectangle
• B. rhombus
• C. trapezium
• D. square

Answer 1

The correct option is A rectangle

We know that in a cyclic quadrilateral, sum of measures of opposite angles is ${180}^o$.

The given cyclic quadrilateral is a parallelogram.

Hence, opposite pairs of angles will be congruent.

$\angle 1+\angle 3={180}^o$ and $\angle 2+\angle 4={180}^o$

$\Rightarrow 2\times \angle 1={180}^o$ and $2\times \angle 2={180}^o$

$\Rightarrow \angle 1=\angle 2={90}^o$

Hence, $\angle 3=\angle 4={90}^o$

Therefore, the given parallelogram has all its angles equal to ${90}^o$ i.e. a rectangle.

Hence, option $A$ is correct.