how do you divide a circle equally~~?

Question

so far all of you are wrong,, youve given me the distance around the circumference,,, forget about the word wrong of divide,,, this is not of importance!! NOW LETS GET TO IT,,

YOU HAVE A 16" CIRCLE,, AND YOU NEED TO MARK OUT 12 EQUALLY SPACED SPOTS ON THAT CIRCLE.... WHAT IS THE FORMULA FOR A STRAIGHT LINE LENGHT BETWEEN SPOTS? FOR THOSE WHO WANT TO GIVE ME THE CIRCUMFERENCE TRY PLOTTING THOSE POINTS ON THE CIRCLE WITH EITHER COMPASS OR RULER? THE CIRCUMFERENCE IS NOT WHAT I NEED!!! WHAT I DO NEED IS THE STRAIGHT LINE DISTANCE ACROSS THE ARC BETWEEN POINTS?



Q

IT IS A 16 INCH DIAMETER CIRCLE. DIDNT I SPECIFY THAT!? COME LETS GET WITH IT,,,,

OK~~DR.D. SPECIFYING 8" RAD.360 DIV. BY 12=30DEG. DIV 16" BY2= 8" CALL THIS AB .STR. LINE BETWEEN POINTS CALL AC IS AT 15DEG RIGHT ANGLE. SO BC=SIN OF 15DEG.TIMES 8" THAN TIMES 2 FOR CHORD LENGTH. WORKING FROM MEMORY SO MAY NEED TO GET TRIG BOOK TO CHECK MYSELF. SO YOU WHERE RIGHT ...JUST WANTED TO SAY THANK YOU FOR ANSWERING ME SO QUICKLY,,

Answer 1

You're saying that what you want is the straight line segment?

Let O = center of circle
Let A and B be adjacent points on the circumference
angle AOB = 360 / 12 = 30
OA = OB = r = 16

So using hte cosine rule on triangle OAB
AB^2 = 16^2 + 16^2 - 2*16*16*cos30 = 68.6
AB = 8.2822 inches

*EDIT*
If 16" is the diameter, then divide my answer by 2.
By hte way, '16" circle' does not necessarily mean 16" diameter. You have to specify, especially with circles. You could have got on with this much earlier if you learn to ask properly.

Answer 2

Your division can be done more accurately with a compass and straight-edge than a ruler or line equations.
From any point on the circle (call it point A) strike an arc of radius R (8"). Call this point C. Bisect the arc of the original circle thus formed, and call this point B. You now have 3 of your 12 points. Go around the circle starting from B striking 8" arcs, (B, C, D, etc.) until you have your 12 points.

BTW the length of the chords is 2*8*sin 15° = 4.1411 inches -- not an easy distance to measure with a ruler.

Answer 3

so there will be 12 wedges. each wedge is somewhat like a triangle, but with the smallest side rounded. like a piece of pizza.

you are asking for the length of the small side of the pizza if you cut the round part off and made it straight--a triangle.

we know the two long sides are of length R (radius of the circle).

we know what the angle is between those two long sides--it is 360 degrees in a circle divided by 12 wedges = 30 degrees.

now we need to do some trigonometry. for a right angle sin()=opposite / hypotonuse. so we have to make our pizza-triangle a right angle by cutting it in half into two smaller pizzas, both with a right angle now.

now the inner angle is 15, (half of 30 since we cut it in half).

so the length of the short end on one of the halves is this equation:

sin(15) = x / radius

if the radius is 8, that comes out to X being 2.07055.

now multiply that by two (because we've only got the halves) to get the full size.

4.1411

so the full equation:

x = diameter * sin(15)

Answer 4

such a line becomes the edge of an isosceles triangle with two equal sides being 16" and the angle between them 360/12 = 30 degrees.

required distance = 2.r.sin15 = 2*16*0.258819045 = 8.28220944"

ur question does not specify whether the 16" is radius or diameter. if its diameter, then required length = 4.14110472"

Answer 5

I haven't seen your previous question but it looks like you need the cosine rule.
Circle divided into 12 means angle at centre =30 deg.
Radius =16
By cosine rule , length of straight line joining points on circumference:
x^2 = 2 x 16^2 - 2x 16^2 cos 30
x^2 = 512( 1 - sqr(3)/2)
x^2 = 68.595 approx
x = 6.282 inches