2019 AMC 10A Problem 6

For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?

- a square

- a rectangle that is not a square

- a rhombus that is not a square

- a parallelogram that is not a rectangle or a rhombus

- an isosceles trapezoid that is not a parallelogram

\textbf{(A) } 1 \qquad\textbf{(B) } 2 \qquad\textbf{(C) } 3 \qquad\textbf{(D) } 4 \qquad\textbf{(E) } 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.