View Full Version : Time for Pythagoras?

clop

2006-Apr-14, 11:44 AM

This is a great graphical puzzle.

Here is quarter of a circle centred at the cartesian origin. We can see the x and y axes. A vertical line drawn upwards from mid-point B touches the circle and then goes across horizontally to point A.

What is the length of the line AB? Please show your working.

http://i48.photobucket.com/albums/f208/tumkin/circleab.jpg

Don't cheat!

clop

randb

2006-Apr-14, 11:52 AM

Let the triangle shown be ABC.

10^2 - 5^2 = 8.66 = BC (This is calculated by connecting the origin O and the point C)

AC = 5

AB^2 = 5*5 + 8.66*8.66

AB = 10

clop

2006-Apr-14, 11:55 AM

Let the triangle shown be ABC.

10^2 - 5^2 = 8.66 = BC (This is calculated by connecting the origin O and the point C)

AC = 5

AB^2 = 5*5 + 8.66*8.66

AB = 10

Hmm very fast. But you didn't need Pythagorus.

clop

Line AB would be the same length as the line that runs from the center of the circle to the point where the tip of the rectangle touches the arc. This means that this line would be 10 units long. 5 from 0,0 to A and 5 from A to the point where the arc crosses the x Axis.

Line AB=raius of circle which is 10. (5+5)

randb

2006-Apr-14, 12:20 PM

lol...i figured that out after I got the answer.

Roy Batty

2006-Apr-14, 03:54 PM

'But it's so simple. All I have to do is divine from what I know of you: are you the sort of man who would put the poison into his own goblet or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me.'

Uh... sorry, wrong question :D

Tobin Dax

2006-Apr-14, 07:41 PM

No Pythagorus, just simple trig: since the cosine of angle A is 1/2, that's a 30-60-90 triangle, and the length of the hypotenuse AB is then the radius of the circle, 10 units.

(BTW, Roy Batty and others who get his joke, go look at absurdnotions.org. Actually, that's amazingly doubly applicable to this thread now.)

Dr Nigel

2006-Apr-14, 08:36 PM

Without having seen any other posts :- 10, because it is equal to the radius of the circle.

Jeff Root

2006-Apr-15, 12:46 AM

I haven't seen anything yet after the words "don't cheat",

though I know there are several replies already.

Informally...

Since the line from B to the circle is vertical, and the line

from there to A is horizontal, you have drawn a rectangle.

The line AB is a diagonal of the rectangle. The other diagonal

(not drawn) goes from the center to the circle, so its length

is 10. The diagonals of a rectangle are equal, so the length

of AB is 10.

-- Jeff, in Minneapolis

Arneb

2006-Apr-15, 10:51 AM

I didn't get it.

What I can tell you is, the name's Pythagoras, not Pythagorus. Even if you don't need him.

clop

2006-Apr-15, 11:22 AM

I didn't get it.

What I can tell you is, the name's Pythagoras, not Pythagorus. Even if you don't need him.

:doh: Sounds very much like a case of sour grapes to me.

clop

Dr Nigel

2006-Apr-15, 04:43 PM

:doh: Sounds very much like a case of sour grapes to me.

clop

No, clop, that was Aesop, not Pythagoras.:)

Tinaa

2006-Apr-15, 06:45 PM

I think there is a special rule for 30/60/90 triangle.

short leg = a

long leg = a * sqrt(3)

hypotenuse = 2a

2a = 2(5) = 10

Arneb

2006-Apr-15, 06:50 PM

:doh: Sounds very much like a case of sour grapes to me.

clop

Oh no, I can live with my mathematical :confused: limitations. Just a case of the nitpicking gene breaking through. No offence :).

Arneb

2006-Apr-15, 06:50 PM

No, clop, that was Aesop, not Pythagoras.:)

:lol:

clop

2006-Apr-16, 07:04 AM

No, clop, that was Aesop, not Pythagoras.:)

No, Dr Nigel, that was Ęsop, not Aesop.:)

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