Logic Puzzles

If the chord (c) is just the diameter of another circle with the same area, you get

A=π r^2 where r=c/2, so
A=π (c/2)^2 = π/4 c^2

Note there's no radius, of either circle, in the result.

Why is the chord the diameter of any circle? That's only true in the case where the chord goes through the centre of the circle.

The rest makes perfect sense. Thanks, I got too hung up with the 2 right-angle triangles formed by bisecting the chord with the radius R i.e., in the circular sector between the chord and circumference.