Posted by dan on Tuesday, January 11, 2011 at 10:00pm.
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?
Drawing a diagram would help with this question.
Thanks.

math  tchrwill, Wednesday, January 12, 2011 at 10:40am
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.

math  dan, Friday, January 14, 2011 at 2:40am
Thank you so much!!
Your explanation was very clear!
Thank you for your help!
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