I have a 18" circle and need it devided into 6 equal pie shapes

Question

I have a 18" peice of plywood cut in a cicle. It is 18" across or 9" to center and need to decorate the out side edge. So I need to figure out how to make 6 equal pie shape peices which will give me my marks for my decoations on the out side edge.

Answer 1

The total circumference is pi*D being D = 18 inches = 56.55 inches. then cut a piece of rope equal to 56.55/6=9.43 inches and mark the points at the end of the rope that has followed the circumference shape and you will have the six pie shape pieces. To cut them, draw a straight line from the center to each one of the points and cut over it. you will have the 6 equal slices. 

Answer 2

This is a very long proof to the final conclusion given in bold at the bottom.

 

 

The key here is some simple geometry & trigonometry. As the person above me mentioned, 360/6=60, which is therefore the measurement of each arc in degrees. Extrapolating from this, we can conclude that the central angle will be 60° as well.

 

The central angle for each arc is a constant equaling 60°

The central angles for each arc is congruent

 

All of the sides of the arcs will of course be congruent because they are radii of the same circle, and since radii of congruent circles are congruent:

 

The sides of each arc is congruent

The measurements of all the sides of the arcs are equal at 9"

 

Now we connect each endpoint of the arcs on the circle to their adjacent endpoints, creating 6 unique triangles. We know that two sides of these triangles are congruent and the angle between these two sides are congruent as well. By the SAS theorem for congruent triangles:

 

All of the triangles created in this way for this circle will be congruent.

 

This has an important implication. Because Corresponding parts of congruent triangles are congruent:

 

The side connecting one endpoint of each arc to its adjacent endpoint is congruent to all of the other sides in this position.

The length between each endpoint of each arc is equal to the corresponding lengths of each other arc.

 

Now, that's fantastic, but it's only worthwhile if we can actually identify this length. It just so happens we can:

 

Let the triangle ABC be a triangle created in the way previously described, where A is the central angle, and B & C are both angles created at the endpoints. 

AB≅AC

Therefore, B≅C because opposite angles of congruent sides are congruent

mA+mB+mC=180; 60+mB+mC=180;2*mB=120;mB=mC=mA=60

Therefore, triangle ABC (and by extension, all other triangles created in this circle this way) are congruent and equilateral with a side length of 9".

 

 

So, a way to do this is to measure a point 9" from a point on the edge of the circle, mark both points, do this 6 times, and connect the dots.

 

Answer 3

360 degrees divided into 6 equal pieces gives each piece 60 degrees.

You could divide the circle in half, then divide each half into 3 equal pieces.

 

You can also use a clock as a reference, and divide the circle into 2:00. 4:00. 6:00, 8:00, 10:00, and 12:00.

or marks on lines from 12:00-6:00, 2:00-8:00, and 4:00-10:00