Middle line trapezoid

[Loki123]

I am curious, say you have an isosceles trapezoid and inside it a circle. Is R (2r) the same as the middle line? Probably not because I can't seem to get the correct answer when I try that, but why isn't it the same?

 

[Dr.Peterson]

I am curious, say you have an isosceles trapezoid and inside it a circle. Is R (2r) the same as the middle line? Probably not because I can't seem to get the correct answer when I try that, but why isn't it the same? View attachment 30586

The important question to ask yourself is, do you have any reason to believe that it is? In math, you can't assume anything without a reason.

The "middle line" you're referring to is presumably the line joining the midpoints of the sides. Does that even look like it should be the same as the diameter of the circle? Are the ends of the diameter you show ever going to be at the midpoints of the sides?

 

[Loki123]

The important question to ask yourself is, do you have any reason to believe that it is? In math, you can't assume anything without a reason.

The "middle line" you're referring to is presumably the line joining the midpoints of the sides. Does that even look like it should be the same as the diameter of the circle? Are the ends of the diameter you show ever going to be at the midpoints of the sides?

My assumption was that the middle line is at the same distance from base 1 and base 2 and that the center of the circle would take on the same role, however, I assume, according to your explanation, the middle line does not always have to be in the middle.

 

[Dr.Peterson]

My assumption was that the middle line is at the same distance from base 1 and base 2 and that the center of the circle would take on the same role, however, I assume, according to your explanation, the middle line does not always have to be in the middle.

No.

Look at a careful picture:

​

The midline of trapezoid ABCD is EF. Does that look like a diameter? Yes, it's equidistant from AB and CD, and it does pass through the center, O. But that's why it can't equal the diameter of the circle, because E and F have to be outside the circle.

 

[Loki123]

No.

Look at a careful picture:

View attachment 30589​

The midline of trapezoid ABCD is EF. Does that look like a diameter? Yes, it's equidistant from AB and CD, and it does pass through the center, O. But that's why it can't equal the diameter of the circle, because E and F have to be outside the circle.

Thank you, I get it