Logic Puzzles

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 chord has some length. I can choose to draw a circle with a diameter of that length. Therefore the chord is the diameter of some circle.

It's deduction. Because the formula exists it must exist for all diameters of room and central column. Therefore you could have a circular room with a 0 diameter column, at which point the chord length is the diameter of a circular carpet,