Geometry problem: six equal angles on a circle

[Leros]

I have a circle, a straightedge, and a ruler. I need to divide the circle into six equal angles. Like this. Suggestions?

I don't wanna do a bunch of bisections, thats too much work. I haven't had geometry in 7 years.

 

[mugs]

Figure out the lengths of the sides of the hexagon that would fit in the circle

 

[Leros]

Originally posted by: mugs
Figure out the lengths of the sides of the hexagon that would fit in the circle

Which is just the radius. Doh.

 

[mugs]

Originally posted by: Leros

Originally posted by: mugs
Figure out the lengths of the sides of the hexagon that would fit in the circle

Which is just the radius. Doh.

Right. So you figured it out?

 

[Leros]

Originally posted by: mugs

Originally posted by: Leros

Originally posted by: mugs
Figure out the lengths of the sides of the hexagon that would fit in the circle

Which is just the radius. Doh.

Right. So you figured it out?

yep.

60 degree angle with two equal sides (the two radiuses) means the triangles are equilateral. So it the edge of the hexagon is the same as other sides, which is the radius.

 

[silverpig]

You could do it with a compass so easily...

 

[Leros]

Originally posted by: silverpig
You could do it with a compass so easily...

I was working on a project. I had a tape measure and a piece of acrylic to use as a straight edge. I don't have a compass or protractor handy.

 

[venkman]

In my day, the teacher gave us a piece of string and a whoopin' to solve this kind of problem.

Kids these days with their fancy cell phones and penicillin.

 

[George P Burdell]

:facepalm;

 

[Skyclad1uhm1]

You can draw a square around it, draw straigth lines between the opposite corners of the square, and you'll have the center of the circle. That way you don't even have to know the radius beforehand.

 

[rezinn]

Draw 6 tangential lines and connect where they intersect?

 

[alkemyst]

Originally posted by: Skyclad1uhm1
You can draw a square around it, draw straigth lines between the opposite corners of the square, and you'll have the center of the circle. That way you don't even have to know the radius beforehand.

That's going to be the right solution. It's going to be the fastest as well.

The hardest part is making sure the square is 'square' to the circle.