Question

true or false? if a circle is circumscribed about a parallelogram, the parallelogram must be a rectangle. a. true b. false

Explanation:

A quadrilateral that can be circumscribed by a circle (cyclic quadrilateral) has opposite angles that are supplementary (sum to $180^\circ$). In a parallelogram, opposite angles are equal. Let each pair of opposite angles be $\angle A = \angle C$ and $\angle B = \angle D$. For the parallelogram to be cyclic:
$\angle A + \angle C = 180^\circ$, so $2\angle A = 180^\circ$, meaning $\angle A = 90^\circ$. All angles in a parallelogram are equal to $90^\circ$ if one is, so it is a rectangle.

Answer:

A. True