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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
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hi Agnishom,

Wasn't that part of the proof from noemi ?

Bob

Children are not defined by school ...........The Fonz

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,182

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

Children are not defined by school ...........The Fonz

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
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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

Children are not defined by school ...........The Fonz

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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: 7,182

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

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
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Are you trying to feed my ego?

Luckily I know you're kidding..

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**bob bundy****Moderator**- Registered: 2010-06-20
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Feed your ego ? What does it eat then ?

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

words that tickle the ears

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

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

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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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