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okay... my attempted diagram.. It probably won't show up correctly when i post it, and confuse everyone more... but i thought I'd give it a shot.
A shaded circle just fits inside a 2m x 3m rectangle. What is the radius in metres, of the largest circle that will also fit inside the rectangle but will not intersect the shaded circle?
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I have a diagram with me, but I don't think it is possible to upload it, so drawing it out would be a good option.
So, from what we can gather from the question, we know the shaded circle is 2 m in diameter. Many assume the the diameter of the largest circle that can fit into the rectangle would be 1 m. However, if pushed the circle in the corner, there is more space, thus the circle MUST be greater than 1m. How to work out exactly what the diameter is, I have no clue.
Anyone who can comprehend what I ranted about up there and explain how I could solve this question will be hailed the ultimate genius.
Thanks.
3 answers
yup.. it didn't work...
it deleted all my spacing..
please ignore the above post.
it deleted all my spacing..
please ignore the above post.
From "A shaded circle just fits inside a 2m x 3m rectangle. What is the radius in metres, of the largest circle that will also fit inside the rectangle but will not intersect the shaded circle?", I assume the circle within the rectangle has a radius of 1 meter.
Drawing a circle in the space between the circle and opposite end of the rectangle, tangent to the two adjacent sides and the circle has a radius of "r".
Relative to the given circle and the circle being sought, we can write
(1 + r) = the distance between the two circle centers
(2 - r) = the distance between the two centers parallel to the long side of 3m
The distance between the two centers parallel to the short side of 2m = (1 + r)^2 - (2 - r)^2 = 6r - 3.
Therefore, r + 6r -3 + 1 = 2 making r = 4/7.
Drawing a circle in the space between the circle and opposite end of the rectangle, tangent to the two adjacent sides and the circle has a radius of "r".
Relative to the given circle and the circle being sought, we can write
(1 + r) = the distance between the two circle centers
(2 - r) = the distance between the two centers parallel to the long side of 3m
The distance between the two centers parallel to the short side of 2m = (1 + r)^2 - (2 - r)^2 = 6r - 3.
Therefore, r + 6r -3 + 1 = 2 making r = 4/7.