I have an arc and want to sketch a rectangle that will be perpendicular to the arc along the center of the rectangle.

I can't seem to apply a perpendicular relationship to a line crossing an arc. How is this accomplished?

When I select a line and an arc should a perpendicular relationship not be available? I only get a tangent.

A two-step process however:

Create a construction line that is tangent, then make your line perpendicular to that line.

or

Create another line that goes through the centerpoint. A line that goes through the centerpoint will always be perpendicular wherever it crosses the circle.