My little dog gets 1/6 of a can of dog food per meal. We usually divide the can into 120º-sectors and scoop halfway down to remove 1/6 of the can. This process involves cutting a circle into 3 equal areas with three cuts.
I realized that a circle can also be divided into 3 equal areas with two perpendicular cuts:
If the diameter of the can is 1 unit, and the colored regions have equal area, can you find the distance AB? I will post each unique solution.
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Ah yea, I think I have a solution!
(WARNING: Spoilers ahead)
My solution is to simply draw two lines from the centre to the corners of the the pink region. That way I have an arc of a circle, whose area is simply dependent on the angle between the two lines I just drew in. (As in 2pi/theta times radius.)
The area of the pink region is the area of my arc of the circle, minus the area of the triangle I created. The area of the triangle can be simply found by the cosine rule (which I can’t remember right now). So just let that equal to 1/3, and solve for theta (the angle).
The rest is trivial trigonometry. If I could remeember the cosine rule (or if I could be bothered to look it up), I might have actually given you the answer. Oh well.