how to calculate the area of a rectangle interstices by a circle

Question

I need to make two calculations: 1. determine to arc that is needed between the two intersection points of a rectangle. Knowns: Size of the rectangle, location of the intersection points; No part of the arc can enter region A to C, and D to B.

2. I want to calculate the area of a rectangle intersected by a arc (see above).

Attached is an illustration of the area I need to calculate.

Answer 1

It is not possible to solve this problem with the information given. Three points are required to define a circle, yet you only have to points.

You can construct multiple possible circles given two points on a rectangle. For example:

Have you been given any extra information about the circle (e.g. radius, diameter, circumference, center, etc.)?