Thread: 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

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

no trig allowed. that takes away a lot of fun problems you know

Originally Posted by Jhevon

no trig allowed. that takes away a lot of fun problems you know

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

-Dan

No, it doesn't.

Trig. makes faster the solutions.

Originally Posted by topsquark

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

-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 i should get around to that one day

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

Well...

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

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

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.

Originally Posted by Krizalid

Hint

Extend by and drop by a perpendicular to that extension.

Hint 2

Use similar triangles.

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

Originally Posted by Krizalid

Hint

Extend by and drop by 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?

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!!

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.

You're assuming the angle is 30° which actually is the answer, but you need to prove it.

i've figured out the solution but the proof doesn't use similar triangles.