# A geometry puzzle

• Had no luck with the "it R Hard" problems myself, but here's one I know the answer to:

Given:

• O is the center of the circle.
• A is at the bisector point of the horizontal line; each half is length 1
• C is on the circumference

The objective is to determine the length of diagonal AB. Only geometric reasoning is required; if you find yourself resorting to algebra or trigonometry, you're on the wrong track.

Hint:

[spoiler]What are the propreties of diagonals of a rectangle?[/spoiler]

[spoiler]Add diagonal OC. This is a radius. We know the radius, which is 2, from the length of OA and its extension, so OC is length 2. Diagonals of rectangles have the same length, therefore AB is also length 2.[/spoiler]

• Without looking at anything else:

[spoiler]
OACB is a rectangle (all right angles).
Hence AB is the same length as OC
OC is the radius of the circle, which is 2.
[/spoiler]

• [spoiler]
AB = OC = 2
[/spoiler]

• heh

• That's too easy.

[spoiler]AB is diagonal of the rectangle OACB, meaning AB = OC. OC is radius of the circle and is clearly equal 2.
Therefore AB = 2
[/spoiler]

BTW, what's up with all these math problems ending up in the "Funny Stuff" section? Math isn't funny. Math is sad.

• Also, WHY THE HELL CAN'T I MAKE A SPOILER? WHAT AM I DOING WRONG!?

Edit: Seems like no new lines allowed. Great.

• paragraphs break spoilers. no blank lines within [spoiler] or sadness

• Math isn't funny

Three statisticians are out hunting when they spot a deer. The first takes careful aim, fires, and sees the bullet go off a foot to the right of the deer.
The second takes careful aim, fires and sees the bullet go off a foot to the left of the deer.
The third one says "We got him, lads"

Why did the cat fall off the roof?
Not enough mu

• The first takes careful aim, fires, and sees the bullet go off a foot to the left of the deer.The second takes careful aim, fires and sees the bullet go off a foot to the left of the deer.

er...

• Three statisticians are out hunting when they spot a deer. The first takes careful aim, fires, and sees the bullet go off a foot to the left of the deer.The second takes careful aim, fires and sees the bullet go off a foot to the left of the deer.The third one says "We got him, lads"

Why did the cat fall off the roof?Not enough mu

• er...

Assume the world is toroidal and 2 feet in length

• Is the deer spherical in a vacuum?

• No, it's vacuum shaped in a sphere

• but is is frictionless?

• Math isn't funny. Math is sad.

• Why did the cat fall off the roof?

Statistically speaking, it's because there was a 62% chance the roof was slippery and an 18% chance that the roof was made of hot tin. The other 20% is because I'm making shit up and can't be arsed to fix the numbers.

• Why did the cat fall off the roof?Not enough mu

That's a physics joke, son.

(I realized after I submitted that this is too obscure. It's supposed to be in a Foghorn Leghorn voice. And, apparently, based on the comics, everyone is "Son" to him.)

• That's a physics joke, son.

Physics is just applied maths

• Physics is just applied maths

Obligatory XKCD

• Physics is just applied maths

• @Jaloopa said:
Physics is just applied maths

fixed that link for you. not that it was wrong per se, just that the mobile site is just as good and works nicer with that hoverover text on mobile.

• Oh, you're on mobile? That's different

• Oh, you're on mobile? That's different

I've done mobile on this site. She has a point about xkcd, too, because it's impossible to view the tool tip in mobile; you need to use their mobile site to to allow you to select a link to see it.

• He has a point about xkcd, too

The fox doth be a vixen, good sir

• This one is trivial:

[spoiler]
BCAO is a rectangle (just from the right angles present and inferrable in the picture), which implies that BA = CO. Since O is the center of the circle and C is on its circumference, CO is a radius of the circle, which makes it and BA both length 2. (BO and CA are both sqrt(3) btw.)
[/spoiler]

• BO and CA are both sqrt(3) btw.

Wrong.

```
BO = CA
BO^2 = AO^2 + AB^2
BO = sqrt(AO^2 + AB^2)
BO = sqrt(1^2 + 2^2)
BO = sqrt(1 + 4)
BO = sqrt(5) = CA

``````
<del>Someone forgot how to use Pythagorean's Theorem.</del>

**Edit**: It's me. :facepalm: I tried doing that off the top of my head and forgot which leg was the hypotenuse.``````

• And he's called @abarker. sqrt(OC² - OA²).

The angles are 30° and 60°.

• It's 2, since it's the same length as the radius of the circle.

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