I am stuck on the following question:
Prove that each diameter is twice as long as each radius.
I drew a circle, with center O and diameter AB. Is there a theorem that could help me say that congruent segment AO and BO add up to form segment AB?
Or is there some other way to prove this?
I would really like it if anyone could give me a hint about this.
Thank you.
$\endgroup$1 Answer
$\begingroup$Hint:
A circle is (in part) defined by having an equal distance from its center to its edge for all points on its edge, i.e. it has a constant radius. So then what's the distance from the edge to the center to the edge again? (And does that sound related to your definition of a diameter at all?)
You could also prove this pretty easily by contradiction: "Suppose $d \neq 2r$. Then..." I'll leave that to you.
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