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How Do You Divide A Circle In 8 Equal Parts Using 3 Lines?

14 Answers

Richard Pratt Profile
Richard Pratt answered
If you count a curve as a line...draw cross hairs on your circle and draw an inner circle through the cross hairs..this divides the circle into 8 equal sections.
Anonymous Profile
Anonymous answered
You can't do this with three lines, but you can do it with three folds.

To get eight equal parts, you have to divide the circle into eight wedge shaped pieces. If you divide the circle in half with one bisecting line, you'll get two pieces. If you draw another line, you can cut those two pieces into four pieces. However, if you draw a third bisecting line, you only cut two of the remaining pieces into four, giving a total of six pieces. Because each line drawn across the circle can only divide two existing wedges into four new wedges, each line drawn creates only two additional wedges.

Imagine you have a circle shaped piece of paper. If you fold it perfectly in half, then open it up, you've bisected the circle once. You'll see one line along the fold that cuts the circle in half.

To get eight parts by way of three folds. Fold the circle in half once like we described above. Fold the resulting half-circle shape in half again. That divides the halves into quarters. If you fold the resulting shape into a wedge shape, that will divide the quarters into eighths. If you unfold your shape, you'll see eight evenly sized wedges, but if you count the actual number of lines used to cut these shapes out you'll see that there are four of them.
Anonymous Profile
Anonymous answered
I'm trying to divide a circle to eight section with three line.
Anonymous Profile
Anonymous answered
Draw two diameter lines intersecting each other and at the center of the intersection draw a circle....YOU SEE you CAN DO IT
Anonymous Profile
Anonymous answered
1st: Cut the cake in half.
2nd: Place the halves on top of each other.
3rd: Cut the halves in half.
4th: Place the fourths on top of each other.
5th: Cut the fourths in half.
That's how you cut a circle cake into 8 equal pieces with only 3 cuts.
Anonymous Profile
Anonymous answered
Uh, the answer by lhm017 is wrong -- only yields 6 pieces. The way to do it involves folding the "pie" onto itself. The first line cuts the pie in half down the middle. Fold one half over the other, and then cut that into half, then half again. Voila! (Hint: The last two lines/cuts should intersect one another. Try it with paper circles or pancakes.)
Oddman Profile
Oddman answered
8 = 2^3, so each cut must cut in half all of the pieces made by the cut before it.
The last cut cannot be a straight line cut.
Anonymous Profile
Anonymous answered
1. Create a straight path at least as long as the radius starting at 0,0;
2. Select (one of) the Reference Point(s) in the Transform Palette yielding 0,0;
3. Ctrl+C and Ctrl+F and select 120 degrees, still in the Tranform Palette;
4. Repeat 2 and 3;
5. Create the circle and move the centre to 0,0;
6. Select all, Pathfinder>Divide, and Control+Shift+G to Ungroup.
Anonymous Profile
Anonymous answered
Without Moving the Cake:

1. Cut the cake in half (vertical cut).
2. Cut the cake in quarters (horizontal  cut).
3. Cut the cake through the middle from the side.

You then have eight pieces of cake, four on the top, four on the bottom.
Tom Smith Profile
Tom Smith answered
Cut the three straight lines horizontally and then draw a circle in the middle.
Or do you mean cut like an X (that makes four parts) and stack the quarters up and then cut in half.

If this circle was 3 dimensional, such as a cake you can make 8 by cutting it into 4 pieces up and down, left and right. ( 12:00 to 6:00, 3:00, 9:00 if it were a clock face) then into a top half and a bottom half.
Like so: (might as well make it a birthday cake)

"------" shows the cut

__i__i__i__i__i_
|happy birthday|
|------|
|______|
Idrees Mukadam Profile
Idrees Mukadam answered
First cut the pie using two cuts in the shape of X,
then cut the pie Horizontally with the last cut and you will get 8 equal pieces of pie.

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