Xmas 2018 Puzzle (4)

L D[AR2P#0.0]

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Divide a circular field into 4 equal parts using three
fences of identical length.


As this answer is pictorial, PM me the length of the fences assuming the diameter of the field is 1 unit.
 
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However, other posts show there are a range of solutions where the diameter of intersecting circles vary e.g. see the below sketch (not to scale)

field2.jpg
 
The solution I was alluding to is two parallel chords, each of which fences off an area of one quarter of the circle. Having done that, a third fence of the same length as the two chords, properly located, and running somewhat diagonally from one chord to the other will bisect the remaining area.
 
1, using squiggly fences.


I like it - bit of a challenge to calculate the path of the squiggle though.


Using fences that extend beyond the boundary of the field means that the question may as well have been:


Code:
Divide a circular field into 4 equal parts using three
 fences.
NB: Diameter of the field was 1 unit
 
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Now if we were to get into a discussion of the definition of a "fence"...

The last post makes me think of this:
Install five fenceposts. One at 12 O'clock, one at 3 O'clock, one at 6 O'clock, one at 9 O'clock, and one at the center of the field.

The first "fence" is a strand of barbed wire 10 cm above the ground that starts at 9 O'clock, runs to the center where it takes a right angled turn and ends at 6 O'clock. Length = D.

The second "fence" is a strand of barbed wire 20 cm above the ground that starts at 6 O'clock, runs to the center where it takes a right angled turn and ends at 3 O'clock. Length = D.

The third "fence" is a strand of barbed wire 30 cm above the ground that starts at 3 O'clock, runs to the center where it takes a right angled turn and ends at 12 O'clock. Length = D.

In a two-dimensional view it looks like two perpendicular lines at right angles intersecting at the center.
 

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