I have a question. It's tied to this (but not this)

View attachment 660520
While it is simple to find the area, I was wondering

**why** it is almost (but a tiny bit less) 2 times the area of the square (roughly 1.9635 times). Maybe

@Grendeldef ?

(a fast way to calculate the area is to drop a vertical from A, to the line OD..., let's say at a point X, and notice that AX=OD, which leads to a line AO^2=5OD^2. And since AO=r, area is 5OD^2 pi/4, roughly 55).