I have a question (given by a teacher) that looks really easy but then when I thought about it, couldn't find a way to find the answer. It is a proof question relating to diameters:
Prove that any two diameters are congruent, and that each diameter is twice as long as each radius.
It seems like common sense, but I can't think of a way to prove it.
Besides this, I also have another question (that I stumbled upon i my reference book) about circles that I could not figure out:
If one chord is a perpendicular bisector of a different chord, then the first chord is a diameter
I think there must be a property relating the center of a circle and the perpendicular bisector of any chord, but I am not sure where to start with this problem.
Any help or hints would be very nice :)