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.



Don't cheat!

clop

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)

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I'm not evil.
An evil person would do the things I think up.

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

'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

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Faber '62 ΔTX
Are you a Bright?

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.)

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

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The quarrelsome oarsmen were rowing,
The great violinist was bowing;
But how is the sage
To tell, from the page:
Was it pigs or seeds that were sowing?

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

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"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

I didn't get it.

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

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Non sunt multiplicanda entia praeter necessitatem.

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

clop

No, clop, that was Aesop, not Pythagoras.

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The quarrelsome oarsmen were rowing,
The great violinist was bowing;
But how is the sage
To tell, from the page:
Was it pigs or seeds that were sowing?

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

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Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

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

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Non sunt multiplicanda entia praeter necessitatem.

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Non sunt multiplicanda entia praeter necessitatem.

No, Dr Nigel, that was Æsop, not Aesop.