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Fixed length from unit square. (Posted on 2009-10-01)

Given a unit square and a fixed length, r.

Construct the set of all points which are at distance r from some point on the square.

Find the area of this set.

Note: A square is composed of 4 line segments, not the interior. For some values of r the set will have a hole in it.

Example of the construction:

No Solution Yet Submitted by Jer

Rating: 5.0000 (1 votes)

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Puzzle Thoughts

Comment 4 of 4 |

The required area is given by:

2*r^2*[arctan(t)-arctan(1/t)] - t + 1

where t = 2*sqrt(r^2 - 1/4) and

arctan returns radians.

Posted by K Sengupta on 2023-06-23 01:42:38

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