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Hi Animesh,

Join R to the centre, O, of the circle. Triangles OPR and OQR are congruent as they have a 90 degree angle and one side in common plus equal radii, OP and OQ.

So OR is a line of symmetry . If OR crosses PQ at S then SP = 3,so RS = 4 by Pythagoras. If you let OS = x and radius = r you can form two equations in r and x by Pythagoras on OPR and on OPS.

It's easier to eliminate r and find x. Then find r.

Alter

Hi sydbernard,

I'm hoping I've understood this. I'm slightly worried by the term disc rather than circle.

Let''s say the disc has radius r and the required circle has radius s. The centre of the disc is O, and the line halfway between the parallels is m.

With centre O and radius r + s an arc cutting m at P will give the required circle centre. So how to 'construct' r + s ?

If m cuts the disc at A, make a line perpendicular to m cutting one parallel at B. AB = s. Extend OA and with centre A and radius AB make an arc to cut OA produced at C. Note: OC = r + s. With centre O and radius OC make an arc to cut m at P P Is the required centre .

But what if the disc is too small to be cut by m ?

In that case you can draw a line n, perpendicular to m, through O. Let n cut the disc at E. Also draw any other line, FG, , parallel to n, so that F is on m and G on the parallel. FG = s.

Join F to E and construct GH parallel to FE with H on n. OE + EH = r + s so once again we have the right radius for an arc to cut m.

Alter

But what does 'exact' mean? If you draw a line 1 inch (or cm) long is that exact? Suppose you look at the line through a magnifying glass. How do you know it is not actually 0.99999 ? I think you are creating an unnecessary difficulty.

A

Hi CIV,

There isn't an exact value for this so you'll have to give an approximate value. On the MathsIsFun main site there is a function plotter. You can plot -x as one line and 2cosx as a curve. Zoom in to get your answer where they cross.

Alter

Hi Abbas 0000

What are you accepting as a 'representation'? If you draw a line and Mark points at regular intervals, labelling them 1, 2, 3, etc you have to assume you can do that accurately. In Euclidean geometry we assume you can, but in the real world there is no such thing as perfect accuracy. Pencil drawn points have size and, by viewing under magnification, you will reveal that drawings are never exact.

So I think what you have described is acceptable. Draw a unit line from zero to point A and then a vertical line up of one unit to point B. With compass point at zero and radius OB make an arc to cut the number line at C. OC is root 2.

This point is as accurate as A, so if the point for 1 is acceptable so is C.

Draw a line vertically up from C one unit, to point D. Compass set to radius OD and make an arc to cut the number line at E. This is root 3.

Repeat the root 2 construction from point E and F will be at root 2 + root 3.

Alter

EOdash = r2

AOdash = d - r2

KJ = r3

AJ = 2r1 - r3

Alter

Say you have an equation in n, where n is a positive integer less than 10000.

A brute force method would be to try every possible value for n, and see which values work.

A

Again no diagram for the first three.

You have correctly found the angle sum for the polygons. In a regular polygon all the angles will be equal, so now calculate one of them.

Your scale factor is correct for small shape as a fraction of the large shape. I think the second answer is for large as a multiple of the small.

In the last a minus sign is needed. I'm not seeing that.

What course are you studying?

A

I don't think it is possible to help without a diagram. Sorry.

A

Hi Animesh,

Write 1000n/810 = d25.d25d25d.......

Subtracting gives 999n/810 = d25

This will greatly simplify and you'll find only one value of d is possible. The value of n follows easily from this

Alter

I thought this was totally sorted by Bob Bundy. Maybe he wasnt clear enough so Ill have a go for him.

Lets call the test availability period, TAP, measured in days.

The professor has declared: Statement = but you won't know in advance which

So on Sunday evening,

As we reach the evening of each day without a test, TAP reduces by 1 and if we count back one day TAP increases by 1.

Deduction one: So by Thursday evening

and so the student deduces that the statement implies the test cannot take place on Friday, soSo far, so good. But then the students logic goes wrong. The students logic, not the professors. Which is at it should be; he is the professor after all. :)

On Wednesday evening

. But the student thinks because of deduction one and counting back one day. And hence the test cannot take place on Wednesday, makingBut you cannot use deduction one on Wednesday evening , because deduction one requires that it is Thursday evening and it isnt. You cannot use logic like this.

In post 56 Bob set up a parallel situation involving his next post. In post 65 he made this post. No one successfully predicted when he would post, but the post occurred. He clearly wasnt lying!

He also said he was giving up on the thread thereafter. Thats why he has asked me to remind everyone about what he said; so he can maintain the position that he was not lying.

I am, of course, happy to assist him.

Alter ego

Agnishom wrote:

Ai do not mean to be rude, but I doubt your identity

What do you mean? I am who I am. I recommend you re-read posts 57 and 66.

Alter

Nice one!

Alter

**alter ego**- Replies: 1

Can somebody help me do

Thanks

hi guys,

You seem to be missing something.

In post 57 bob said he would post during the week but you wouldn't know when.

In post 66 he posted. It was a Tuesday. Nobody predicted that.

He also said "So, I'll have one last go and then I'm giving up on this thread."

So he is clearly not going to come back to this thread again.

Case closed.

alter ego

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