Basic mathematical laws on circles needed.

**Zanx** · 10-10-09, 19:11

I've Googled it but don't even know how to put the question.

I need to know if A in the attached pic and the yellow line, will always be linked somehow to the size of the circle.

Circle is 5000mm, what will A always be and what will the yellow line always be?

Apologies for the plebby question, maffs was never my strong point.

**irie** · 10-10-09, 19:20

Squaring the circle - Wikipedia, the free encyclopedia

**chillitt** · 10-10-09, 19:22

Diameter is 5000, so radius is 2500. a squared plus b squared equals c squared, so 2500x2500 + 2500 x 2500= A squared.
I dont have a calculator handy so you can do that bit.

**saga_lout** · 10-10-09, 19:23

Pythagoras, he say:
A squared = 2500 squared + 2500 squared
Yellow line squared = A/2 squared + (2500 - A/2) squared

(I think)

That's the maths. I'll leave you to do the arithmetic.

**Screwdriver** · 10-10-09, 19:28

What you need is to search for "chord" which is the name of the straight line in your circle.

Calculation here:
If the angle between the two radii from the ends of the chord is A, and the radius of the circle is R, the chord length L will be
L = 2RsinA/2. You can prove this easily by joining the point bisecting the chord to the centre, you then have two rightangled triangles, with an included angle of A/2, and an opposite side of L/2. So sinA/2 = L/2R.

From: WikiAnswers - What is the Formula for calculating chord length

Screwd.

**Silly Car** · 10-10-09, 19:30

C= 5000/2 x Pi
= 795.78

Angle between C&C = 360/8 = 45 degrees
Using

B=775.36

I'm fucked if I can remember ho to calculate A

**DefTrap** · 10-10-09, 19:30

Using pythagoras A(squared) + B(squared) = C(squared)
A = B in this case as it's a right angled triangle with 2 equal sides
therefore 2A(squared) = 5000(squared)
therefore A = 3535.53

For the yeller line we know that an interior angle of an octagon = ~~120~~ 135deg and the opposite side A = 3535.53
You can make a right-angle triangle using 1/2 the A line and the yellow line and using trigonometry again can work out that yellow = 2041.24

So I make red = 3535.53 and yellow = ~~2041.24~~ 1913.42

Edited: at least I showed my working. Half marks.

**Kyot** · 10-10-09, 19:31

Octagon is 135º no?

**DefTrap** · 10-10-09, 19:35

Doh. Yeh 135.
So yellow = 1913.42 ?

**Screwdriver** · 10-10-09, 19:35

A is 4254.5 in this case. Working on <yellow>

Screwd.

**Silly Car** · 10-10-09, 19:38

Originally Posted by Silly Car

C= 5000/2 x Pi
= 795.78

Angle between C&C = 360/8 = 45 degrees
Using

B=775.36

I'm fucked if I can remember how to calculate A

Bollox

A= 1125.40

Using Pythagoras properly

**Screwdriver** · 10-10-09, 19:38

Yellow is 2435.9mm

Screwd.

**Silly Car** · 10-10-09, 19:39

Originally Posted by DefTrap

Doh. Yeh 135.
So yellow = 1913.42 ?

Just multiply that by 8 and see where you get

Screw'd, nope on both counts (try multiplying yellow by 8 )

**Screwdriver** · 10-10-09, 19:42

They will always be in proportion so you can divide the answers by 5000.
The correct calculation is Sin <angle of chord> times diameter.

If A was indeed 1125 then A would be about a fifth of the diameter!

Screwd.