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Let there be a Triangle ABC and O a point inside it

Prove that:

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,536

hi Agnishom,

Wasn't that part of the proof from noemi ?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

Let

.*Last edited by noemi (2012-09-08 22:41:17)*

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Explain step by step Please.....

How do you get this ---> BO + OC < BP + BC ?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,536

It's an excellent proof by noemi. I shall humbly try to explain it.

Extend BO until it cuts AC. Call this point P.

In triangle OPC, OC < OP + PC

so

OB + OC < OB + (OP + PC) = (OB + OP) + PC

But B, O and P make a straight line so replace OB + OP with BP

OB + OC < BP + PC

In triangle ABP, BP < BA + AP

so

OB + OC < (BA + AP) + PC = AB + (AP + PC)

But A, P and C make a straight line so replace AP + PC with AC

OB + OC < AB + AC

Brilliant, noemi,

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

thank you Bob, great explanation.. I started drawing, but then I saw your post

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**bob bundy****Moderator**- Registered: 2010-06-20
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hi noemi

Note that your one liner took my little brain 8 steps!

I stand in awe. (well sitting actually)

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

I agree that I should have been more detailed

I hope Agnishom is satisfied now

*Last edited by noemi (2012-09-09 01:51:47)*

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Thanks! Thanks! Thanks!

Please see this and tell me if I realised it correct:

Adding OB to both sides,

------> Statement 1

In Triangle ABP:

Adding PC to both sides,

----> Statement 2

From Statement 1 & 2,

Yahoo!

P.S: There was a little bug, I just edited this post

*Last edited by Agnishom (2012-09-09 02:05:16)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,536

noemi wrote:

I agree that I should have been more detailed

You have misunderstood my comment. It wasn't a criticism.

I am in awe because you thought all that in one line.

I had to try to follow each step, spend a while doing that, then re-write it in several steps for my little brain.

I make that 1 noemi brain = 8 times a Bob brain.

Bob

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

Are you trying to feed my ego?

Luckily I know you're kidding..

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,536

Feed your ego ? What does it eat then ?

Bob

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

words that tickle the ears

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,536

That doesn't seem wise to me.

http://voiceciw.hubpages.com/hub/Most-R … s-The-Ears

I am inclined to 'tell it like it is' or keep schtum.

Perhaps your 'super-ego' will see the wisdom in this.

Bob

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

Amen to that article! I'm pleasantly surprised that you've sent it

Actually my point was ..that you were overreacting with compliments.. I know you were joking, but we must be careful with every word..

It's easy to tickle ppl's ears..

but don't worry..I'm not overestimating myself, actually I'm very self critical

*Last edited by noemi (2012-09-09 07:32:49)*

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Is that article about psychology or religion?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**noemi****Member**- Registered: 2010-01-07
- Posts: 2,333

It's about Bible verses

(2 Timothy 4:3-4)

3 For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears;

4 And they shall turn away their ears from the truth, and shall be turned unto fables.

*Last edited by noemi (2012-09-10 02:09:32)*

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