posted by dan

I'm not sure whether this question is too difficult, or perhaps it is lacking a diagram, but I have been getting no response to this question, something I had not been not expecting.

To any maths experts out there, I would absolutely LOVE your help, because I just can't get my head around this one.

Here it is:

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?

If you believe a diagram would help, I could try and upload the diagram onto photobucket and give you the link.

Be my saviour!

Thanks!

1. MathMate

First, the first circle that "just fits" inside the rectangle is tangent to only three sides, the two long sides and one short side. Call its radius R, and the centre A.

The second circle will be tangent to the opposite short side, one of the long sides and the first circle. Call the radius of the second circle r, and the centre B.

Join the centres of the two circles, AB, and drop perpendiculars parallel to the sides of the rectangle until they meet. Call this point C.

Thus we have a right triangle ABC, right-angled at C.

We have the following information:
R=(short side)/2=1
AB=R+r
AC=R-r
BC=sqrt(AB²-AC²)

By equating the length of the long side with the sum of R,BC and r, you can solve for r:
R+BC+r = long side = 3

Post if you need a diagram.

2. dan

I'm still stumbling over where point C is. "Drop perpendiculats parallel to the sides of the rectangle until they meet".

A diagram would most definately be helpful.

Once again, thank you for your help.

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