Can this simple circle question be maths solved ?

Steve · Joined: 05 Aug 2007 Posts: 3

Hi, I am not going to dust off my pure maths books after 35 yrs of being out
of school. Anway I dont have them !
I am sure there is a maths fix to this question.

Q1) If there are eight circles each 25mm diameter, in circular orbit about
a centre point, (i.e they all are the same distance out from the centre
point) with shortest distance between any two adjacent circles of 9.74mm,
what is the distance from centre point to the centre of one of those circles
?

I am faced with trial and error on a vector prog to solve this otherwise Sad

Many thanks.
Steve

Archived from group: uk>education>maths

Ken Pledger · Joined: 05 Aug 2007 Posts: 9

In article ,
"Steve" wrote:

> ....
> Q1) If there are eight circles each 25mm diameter, in circular orbit about
> a centre point, (i.e they all are the same distance out from the centre
> point) with shortest distance between any two adjacent circles of 9.74mm,
> what is the distance from centre point to the centre of one of those circles
> ? ....

This seems to mean that the distance between the centres of two
adjacent circles is 25 + 9.74 = 34.74 mm. Is that right?

If so, then consider the triangle whose three vertices are those
two centres and the main centre of the diagram. One of its sides has
length 34.74 mm, the other two sides have the unknown length you want,
and the angle between these is 45 degrees. Applying the cosine law to
that triangle and doing a bit of algebra gives the length you want as

(34.74)/sqrt(2 - sqrt(2)) which is about 45.39 mm (E. & O. E.)

Ken Pledger.

Steve · Joined: 05 Aug 2007 Posts: 3

Many thanks, that indeed is so and understood by you.
Now why didnt I think of it that way !
In fact another way I now see is its the hypo of a triangle 22.5deg at
centre of orbit and half of 34.74mm t'other end.
Thanks
Steve

"Ken Pledger" wrote in message@bats.mcs.vuw.ac.nz...
> In article ,
> "Steve" wrote:
>
> > ....
> > Q1) If there are eight circles each 25mm diameter, in circular orbit
about
> > a centre point, (i.e they all are the same distance out from the centre
> > point) with shortest distance between any two adjacent circles of
9.74mm,
> > what is the distance from centre point to the centre of one of those
circles
> > ? ....
>
>
> This seems to mean that the distance between the centres of two
> adjacent circles is 25 + 9.74 = 34.74 mm. Is that right?
>
> If so, then consider the triangle whose three vertices are those
> two centres and the main centre of the diagram. One of its sides has
> length 34.74 mm, the other two sides have the unknown length you want,
> and the angle between these is 45 degrees. Applying the cosine law to
> that triangle and doing a bit of algebra gives the length you want as
>
> (34.74)/sqrt(2 - sqrt(2)) which is about 45.39 mm (E. & O. E.)
>
> Ken Pledger.

simple(?) algebra question Hi, wish I'd have paid more attention at school - who would have thought algebra would actually come in useful in the real world! Just need help with this - if x = (a-b)/b then how do I rearrange it to find out b if I know a and x?

Maths Question This has bugged me since I was a small boy. I know it works, but never fot any mathmatical explanation of how. Basically there are 4 pieces of card, which can be arranged to make a shape that has a total area of 63cm squared. If you rearrange them, the s

3d maths question Can anyone help with what should be a simple 3d problem? I have a 3 sided polygon that it being hit by a vector. I already know how to calculate the point of intersection between the two, and I need to calculate a vector that lies on the face of the poly

Kids' maths question - help! A colleague's child has been set the following: There are 3 hens: A & B together lay 10 eggs B & C together lay 14 A & C together lay 12 How many does each lay? We know the answer is 4, 6 & 8, but can't demonstrate a mathematical way of showing it. It lo

question about TI84 Plus SE in AQA A Level Maths exams Hello, I'd be grateful if someone could tell me whether use of the TI84 Plus SE calculator is allowed in AQA A Level exams. I have asked AQA and they just say what is not allowed, namely CAS calculators and ones that are rigged up to communicate with the