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.

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To find the radius of the largest circle that will fit inside the rectangle but will not intersect the shaded circle, we need to consider the dimensions of the rectangle and the shaded circle.

Let's assume the shaded circle has a radius of r meters. Since it is stated that the shaded circle just fits inside the rectangle, the diameter of the shaded circle must be equal to the length of the shorter side of the rectangle. In this case, the shorter side is 2 meters. Therefore, the diameter of the shaded circle is 2 meters.

Since the diameter of a circle is equal to twice the radius, we can calculate the radius of the shaded circle as r = 2/2 = 1 meter.

Now, to find the maximum radius of the circle that can fit inside the rectangle without intersecting the shaded circle, we need to find the longest possible radius that does not surpass the shortest dimension of the rectangle (2 meters).

So, the maximum radius of the circle will be equal to half of the shorter side of the rectangle, which is (1/2) * 2 = 1 meter.

Therefore, the largest circle that will fit inside the rectangle without intersecting the shaded circle has a radius of 1 meter.

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.