Silly Geometry question!

[Videoorchard]

Hey,

Please refer this pic:
http://goo.gl/V81SUC

If a circle is inscribed inside a rectangle and length of the diameter of the circles is 6, then can we assume/say that all the 4 sides of the rectangle also has a value of 6?


Thank you for answering! :)

[n00bpron00bpron00b]

At-least 2 sides of the rectangle will have same length as 6 (depending on the orientation of diameter) and if any additional information is given.

Also, square is special case of rectangle & rhombus = there could be a possibility where all sides of the rectangle are 6. (i.e. Area of a rectangle is max when it becomes a square)

It all depends on the problem asked/information given.

[Videoorchard]

Hi Noob,

Thank you for answering. :) I guess my question wasn't framed properly. So my original question was, because the circle touches the rectangle in all the 4 sides, from the first figure, can we infer/ can we rotate the segment(diameter) of the circle from horizontal to vertically to get the other sides of the rectanlge? :)

[tommywallach]

Hey Video,

The point is that it's "inscribed" even if it's only touching TWO sides (i.e. the top and bottom, but not the sides), so it depends if the question is specifiying that it's inscribed in a SQUARE (in which case, the answer to your question is of course yes, we can rotate). If it's not a square, then the other two sides might not be.

This video will show a picture of what I/we mean (I didn't listen to the video, I just saw the picture, so ignore the actual video, as I have no idea what's in it): https://www.youtube.com/watch?v=ATY6vlsHiM0

-t

[Videoorchard]

Hi Tommy,

Thank you so much for answering!

The point is, the circle touches all the 4 sides of the rectangle. Now, we know that the length of the diameter(Horizontally) of the circle to be 6. Hence we can conclude that side of the rectangle(horizontally) to be 6 as well.

Now, can we take this to one step furthur and infer this:

Hmm. Let's flip the diameter of the circle i.e 6. vertically (Since diameter of circle are same vertically or horizontally, in a circle). Hence we can conclude that the vertical sides of the rectangle is 6 as well.

Could you point out where i am going wrong in this tommy?

P.S: I am quite confident on how things work in square, because in square, if we know atleast one side, then we can infer all the other sides are the same as well. :)

[tommywallach]

Video,

A circle can't touch all 4 sides unless it's a square, because a circle is perfectly symmetrical. If it's a rectangle, it doesn't touch all 4 sides, so though you know that 2 sides are equal to the diameter, you literally have no idea the length of the other two sides. Does that make sense?

-t

[Videoorchard]

i got it now! *Eureka :) Thank you!

[tommywallach]

Glad to! : )

-t

[n00bpron00bpron00b]

A circle can't touch all 4 sides unless it's a square, because a circle is perfectly symmetrical. If it's a rectangle, it doesn't touch all 4 sides, so though you know that 2 sides are equal to the diameter, you literally have no idea the length of the other two sides. Does that make sense?

Perfect ! Thanks

[tommywallach]

Good convo!