In the xy plane, a circle has its center at the origin and a radius of 5. What is the length of the shortest line segment that has one endpoint on the circle and the other at (13,0)?
How does radius mean diameter here??
I don’t see “diameter” anywhere in the question. So I have no idea what you’re asking…
Why would radius mean diameter? There’s a circle. It’s centered on the origin. It stretches out five units in each “cardinal direction” – +y, -y, +x, -x. (13,0) is a point 13 units right of the origin on the x-axis. They’re asking for the shortest distance from any point on the circle to (13,0).
Is the answer 8 or am I missing something?
^Yeah it’s 8.
Yeah you’re right. I was just thinking that radius equals twice the diameter (or am I wrong).
Radius is half the diameter, or diameter is twice the radius.
I didn’t think about the diameter at all on this problem. I pictured the graph, and it seemed obvious that the circle crosses the x axis at (5,0). A straight line from there to (13,0) is going to be 8 long.
What I meant was that it said radius of 5, so the diameter must be 10. Thus, the distance from (10,0) to (13,0) is 3. However, my traditional understanding of the word radius turned out to be wrong in this specific instance.
Traditional? Please unpack that a bit—this is a completely standard term with precisely one meaning, as far as I’m aware.
Warning: Students studying for a geometry test (or any other test, for that matter) should read this thread with caution, and maybe not at all.
dfbdfb, I wouldn’t read too much into that. It hearkens back to this gem of a few days ago: “Though my opinion is really a fact, some colleges may beg to disagree.” It seems OP doesn’t like to be wrong. 
The diameter is 10… So the circle goes from (-5,0) to (5,0) on the x axis. It is not relevant to solving this problem, though.
That is very helpful - thanks @intparent .