# Geometry challenge #2

David113
Posers and Puzzles 20 Oct '07 22:42
1. 20 Oct '07 22:42
Given a circle, divide it into 4 equal arcs using only a compass.
2. wolfgang59
Mr. Wolf
21 Oct '07 05:45
Draw a line from North to South and another from East to West.

ðŸ˜‰
3. 21 Oct '07 05:50
Originally posted by wolfgang59
Draw a line from North to South and another from East to West.

ðŸ˜‰
lol... i like that.... works for me
4. 21 Oct '07 08:12
Originally posted by David113
Given a circle, divide it into 4 equal arcs using only a compass.Originally posted by wolfgang59
Draw a line from North to South and another from East to West.

ðŸ˜‰
How do you draw a straight line with "only a compass"?
5. wolfgang59
Mr. Wolf
21 Oct '07 10:38
Originally posted by FabianFnas
How do you draw a straight line with "only a compass"?
He didnt say the line had to be straight!
6. wolfgang59
Mr. Wolf
21 Oct '07 10:45
Originally posted by David113
Given a circle, divide it into 4 equal arcs using only a compass.
OK he we go ...

1. Assuming you mean compasses and not compass.

2. Assuming we have a straight edge to hand.

Draw two circles (B & C) of equal diameter with centres on the circle in question (A). Draw a line through the points of intersection of B & C. This will be a diameter of A. Call the intersections of this diameter with A points x & y.

Now draw circles (D & E) of equal diameter with centres on x & y. Connecting the intersections of D & E wil give another diameter of A which is orthogonal to the first diameter.

Hence the original circle is now exactly quartered.
7. 21 Oct '07 11:06
Originally posted by wolfgang59
OK he we go ...

1. Assuming you mean compasses and not compass.

2. Assuming we have a straight edge to hand.

Draw two circles (B & C) of equal diameter with centres on the circle in question (A). Draw a line through the points of intersection of B & C. This will be a diameter of A. Call the intersections of this diameter with A points x & y.
...[text shortened]... hich is orthogonal to the first diameter.

Hence the original circle is now exactly quartered.
Yes, compasses ðŸ˜µ
We do not have a straight edge.
8. AThousandYoung
22 Oct '07 00:16
Make the compass radius equal to circle diameter by having it span the circle and then rotating it. If it has the same radius as the circle diameter, when rotated it will touch the circle only at one point, tangentially, and that will be the diameter. This gives you two points opposite one another, which splits the circle into halves.

Now, hang the circle vertically such that these two points are on a horizontal line. Remove the little pencil from the compass, draw the horizontal, and then stand the little pencil on the line. The base of the pencil is at 90 degrees to the shaft. Using the pencil as a straight edge, find out what the highest point on the circle is relative to the pencil (remember, the circle is vertical now). That point is halfway between the others. Use the compass to find it's opposite as with the first two.
9. 22 Oct '07 09:171 edit
Originally posted by AThousandYoung
Now, hang the circle vertically such that these two points are on a horizontal line...
Since you appear to have a spirit level, you might as well use that as your straight edge, making the problem much simpler ðŸ™‚
10. wolfgang59
Mr. Wolf
22 Oct '07 09:50
Originally posted by AThousandYoung
Make the compass radius equal to circle diameter by having it span the circle and then rotating it. If it has the same radius as the circle diameter, when rotated it will touch the circle only at one point, tangentially, and that will be the diameter. This gives you two points opposite one another, which splits the circle into halves.

Now, hang t ...[text shortened]... nt is halfway between the others. Use the compass to find it's opposite as with the first two.
compasses compassES !!!! ðŸ˜
11. AThousandYoung
25 Oct '07 14:23
Originally posted by mtthw
Since you appear to have a spirit level, you might as well use that as your straight edge, making the problem much simpler ðŸ™‚
No need for a level. The horizontal state can be approximate. I'm relying on the pencil's base being perpendicular to it's shaft.
12. 25 Oct '07 14:37
Originally posted by AThousandYoung
No need for a level. The horizontal state can be approximate. I'm relying on the pencil's base being perpendicular to it's shaft.
You sure about that? Right-angled to approximately level will only give you approximately the highest point.

Anyway, better hope that the pencil doesn't have an eraser on the end. Or been chewed. All seems very approximate to me.
13. 25 Oct '07 14:38
Originally posted by wolfgang59
compasses compassES !!!! ðŸ˜
'Compass' is acceptable according to the OED, although is says compasses is more common. ðŸ™‚
14. 25 Oct '07 15:541 edit
Draw the circle, and carefully maintain the same radius.

Use the compass, with the same radius and mark a point anywhere on the circumference.

Draw line one, through the the point on the circumference and the centre point dividing the circle into equal lhalves.

Draw line two, now expand the compass, placing the point at the position where this dividing line intersects the circumfernce and make it wider than the diameter. now complete a full circle.

Draw line three, repeat line two but from the opposite side.

Draw line four, now you have three circles, the outer two will overlap at the top and bottom, a line through these points and the original centre
will perfectly divide the circle into four equal arcs.

edit for spelling
15. 25 Oct '07 16:14
Originally posted by kcams
Draw the circle, and carefully maintain the same radius.

Use the compass, with the same radius and mark a point anywhere on the circumference.

Draw line one, through the the point on the circumference and the centre point dividing the circle into equal lhalves.

Draw line two, now expand the compass, placing the point at the position where this dividin ...[text shortened]... the original centre
will perfectly divide the circle into four equal arcs.

edit for spelling
Two problems:

- You're given the circle, you don't get to know where the centre is.

- A straight edge (needed to draw any straight lines) is not available. A solution has already been posted if you have one.