Are each of the following statements for chords, radiuses, diameters and arcs of a circle true?

Question

Are each of the following statements for a circle true?

1. If a radius bisects a chord, then this radius is perpendicular to this chord.
2. If a radius is perpendicular to a chord, then this radius bisects this chord.
3. If a radius bisects a chord, then this radius bisects a corresponding arc.
4. If a radius bisects a arc, then this radius bisects a corresponding chord.
5. If a radius is perpendicular to a chord, then this radius bisects a corresponding arc.
6. If a radius bisects a arc, then this radius is perpendicular to a corresponding chord.

Are each of these statements true for a diameter instead of the radius?

What if the chord is a diameter? Are each of these statements true in this case?

Answer 1

They are definitely all true. Any straight line going through the center of the circle has to be perpendicular to a chord if it bisects it. To bisect it, after all, it must split it into two equal parts. This works for diameters as well, yes. Most of these situations follow the same logic as others.

I suggest drawing chords and seeing if you can create a radius that is not perpendicular to them but must also split them into equal parts. It is impossible, I guarantee (unless you draw ovals or some other shapes).