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!

## Answer this Question

## Related Questions

- math - A shaded circle just fits inside a 2m x 3m rectangle. What is the radius ...
- 11th grade specialist math - I'm not sure whether this question is too difficult...
- math - find the shaded area in the circle with a rectangle ( 3 x 4 ft dimension...
- geometry - A dartboard consists of a circle inside a rectangle. the diameter of ...
- math - The length of the rectangle is 20 m and the width of the rectangle is 10 ...
- Math 5th grade - Sorry for re-post. Damon answered but I do not see any relate ...
- MATH - I have been given a circle with a shaded triangle. Inside the circle is ...
- 10th grade - Find the area of the shaded region. the outter shape is a rectangle...
- Math - Marian drew a picture of two circles.She wanted to shade only the outer ...
- Math - Working on patterns. There is a diagram. Its a rectangle with the numbers...