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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