Or what is the combined area of the circle segments (chords)?
Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the distance between the circle centre and the corners of the square is the radius). The top edge of the square is tangent to the top of the circle, so you have a square which covers all of the circle except for 3 chords (2 of which are equal).
It would probably help to draw it!
I have a solution for this, but I am afraid that it is not a simple one.
Referring to the diagram below:-
The vertical length of the square = the green line = R + R cosθ
The horizontal length of the square = 2 R sinθ
∴ 2 R sinθ = R + R cosθ
If we let 2x = θ, then 2 (2 sin (x) cos (x)) = 2 cos2 (x)
∴ Cos (x) [cos (x) – 2 sin (x)] = 0
Rejecting the solution for cos (x) = 0 and obtain tan (x) = 1/2
Once x (and hence θ) is known, then the rest is found by:-
Area of the segments combined
= area of the circle – area of the square + 2 * area of the yellow shard part
Area of the yellow shaded part
= area of quad OPCQ – area of OQS – area of sector OPS
= R(R sinθ) – (0.5)(R sinθ)(R cosθ) – Rθ