i need more help with math

Question

Select the correct answer.

Cathy constructs diameter  of circle O and then constructs the perpendicular bisector, , of . Which construction can she complete?

A. 

an equilateral triangle inscribed in a circle

B. 

a regular hexagon inscribed in a circle

C. 

an isosceles trapezoid inscribed in a circle

D. 

a square inscribed in a circle

Answer 1

The answer is D. Quadrilateral AXBY is a square. One way to prove this is:

A. m∠AOX, m∠BOX, m∠BOY, and m∠AOY are all 90-degrees since AB and XY are perpendicular.

B. OX = OY = OA = OB since AB and XY are diameters and bisect each other.

C. Thus, △AOX, △AOY, △BOY, and △BOX are all congruent due to the SAS property.

D. Thus, AX = BX = AY = BY because corresponding parts of congruent triangles are congruent.

E. We also know that m∠XAY, m∠AXB, m∠XBY, and m∠BYA are all 90 degrees because inscribed angles from the diameter are right angles.

From D and E, we have a quadrilateral with four congruent sides and four 90-degree angles. That's one of the definitions of a square.

UPDATE: And I guess C is a valid answer too, since a square is a form of an isosceles trapezoid. If you're allowed multiple answers, then put C and D. If just one answer is allowed, then put D because it is the most specific.