# Geometry Marathon

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• Jun 8th 2007, 02:44 PM
Krizalid
Geometry Marathon
(Perfect Hacker: I hope you allow this)

Geometry it's beautiful!!!

Let's start a G-M

You know the rules, person who solves the problem, proposes the another one, but before proposing it, he must have the approval (if the answer is correct or not) of the person who proposed the previous geometry problem.

... and don't forget -no trig. allowed-. Use LaTeX.

Here's the first one

http://img89.imageshack.us/img89/2872/problem001bz3.gif
• Jun 8th 2007, 02:54 PM
Jhevon
Quote:

Originally Posted by Krizalid
(Perfect Hacker: I hope you allow this)

Geometry it's beautiful!!!

Let's start a G-M

You know the rules, person who solves the problem, proposes the another one, but before proposing it, he must have the approval (if the answer is correct or not) of the person who proposed the previous geometry problem.

... and don't forget -no trig. allowed-. Use LaTeX.

Here's the first one

http://img89.imageshack.us/img89/2872/problem001bz3.gif

no trig allowed:eek:. that takes away a lot of fun problems you know
• Jun 8th 2007, 02:55 PM
topsquark
Quote:

Originally Posted by Jhevon
no trig allowed:eek:. that takes away a lot of fun problems you know

What? You don't own a (signed) copy of "The Elements?" :eek:

-Dan
• Jun 8th 2007, 02:55 PM
Krizalid
No, it doesn't.

Trig. makes faster the solutions.
• Jun 8th 2007, 03:08 PM
Jhevon
Quote:

Originally Posted by topsquark
What? You don't own a (signed) copy of "The Elements?" :eek:

-Dan

lol, no i don't own a signed copy. don't own an unsigned copy either. in fact, never read it, or even a part of it:o i should get around to that one day

Quote:

Originally Posted by Krizalid
No, it doesn't.

Trig. makes faster the solutions.

well i think trig is fun, and most of the geometry i'm used to, involves trig. although, i haven't done geometry as a class to itself for a while now, maybe i'm forgeting what it entails
• Jun 8th 2007, 05:46 PM
Krizalid
Well...

Does anybody need a Hint?, or you wanna try it by yourselves?
• Jun 9th 2007, 08:37 AM
topsquark
Quote:

Originally Posted by Krizalid
Well...

Does anybody need a Hint?, or you wanna try it by yourselves?

It's a deuce of a figure to try to construct... (without knowing the answer, that is.)

-Dan
• Jun 9th 2007, 05:36 PM
ThePerfectHacker
Quote:

Originally Posted by Jhevon
i should get around to that one day

The Elements is the greatest book written by a man. It is a kollasal size of 13 volumes. I would image hundreds of years ago people memorized each line, each word, each proof what the Great One* has written. People should have a lot of respect when they refer to that book.

*)Translation: Euclid of Alexandria.
• Jun 12th 2007, 01:27 PM
Krizalid
Quote:

Originally Posted by Krizalid

Hint

Extend $\displaystyle \overline{BD}$ by $\displaystyle D$ and drop by $\displaystyle C$ a perpendicular to that extension.

Hint 2

Use similar triangles.
• Jun 12th 2007, 02:37 PM
topsquark
An interesting idea....

(Of course, even if I get the proof I can't legally post it since I don't have one for to continue this. Ah well!)

-Dan
• Jun 12th 2007, 03:25 PM
OReilly
Quote:

Originally Posted by Krizalid
Hint

Extend $\displaystyle \overline{BD}$ by $\displaystyle D$ and drop by $\displaystyle C$ a perpendicular to that extension.

Hint 2

Use similar triangles.

I am not sure what is the solution.
It seems like there is lack of information.

Can you post the solution?
• Jun 12th 2007, 03:54 PM
Krizalid
That's what you think, but it's not...

This is not an easy geometry problem (well in fact, I've got hard ones)

Try it!!
• Jun 15th 2007, 03:04 AM
Janner
I don't have any fancy programs to d othe things you do, not yet atleast.

ΔBCD = 180 degrees,
<BDC = 180-45 = 135 degrees,
<BCD = 180 - 135 - x = 45 - x

ΔABC = 180 degrees,
<ABC = 180 - x - <BCA

ΔABD = 180 degrees,
<ABD = 180 - 45 - x = 135 - x

x = 30 degrees?
If that is true, <DBC must be 45 - 15 = 30, if that is true
ΔBCD = <BDC + <DBC + <BCD = 180 degrees
ΔBCD = 135 + 30 + 15 = 180 degrees

I could very well be wrong 'cause I'm just 14, and my notation sucks. The way I wrote it is understandable for me, but it may not be for others. It could also be that this is no proof at all, just some facts written down. If I happen to be right, someone else can go as I don't think I could make a good looking and well-thought problem.
• Jun 15th 2007, 07:45 AM
Krizalid
You're assuming the angle is 30° which actually is the answer, but you need to prove it.
• Jun 22nd 2007, 05:36 AM
blurgh
i've figured out the solution but the proof doesn't use similar triangles.
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