Another Triangular Problem

Agnishom · 2012-09-08 14:06:19

Let there be a Triangle ABC and O a point inside it
Prove that:

Bob · 2012-09-08 19:43:40

hi Agnishom,

Wasn't that part of the proof from noemi ?

Bob

noemi · 2012-09-08 22:38:47

Let

.

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

Agnishom · 2012-09-09 01:16:44

Explain step by step Please.....

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

Bob · 2012-09-09 01:29:50

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

noemi · 2012-09-09 01:34:59

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

Bob · 2012-09-09 01:36:56

hi noemi

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

I stand in awe. (well sitting actually)

Bob

noemi · 2012-09-09 01:40:16

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)

Agnishom · 2012-09-09 01:54:44

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)

noemi · 2012-09-09 03:35:04

Bob · 2012-09-09 04:37:18

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

noemi · 2012-09-09 04:55:21

Are you trying to feed my ego?
Luckily I know you're kidding..

Bob · 2012-09-09 06:53:02

Feed your ego ? What does it eat then ?

Bob

noemi · 2012-09-09 07:03:19

words that tickle the ears

Bob · 2012-09-09 07:15:27

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

noemi · 2012-09-09 07:31:55

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)

Agnishom · 2012-09-10 00:09:22

Is that article about psychology or religion?

noemi · 2012-09-10 01:35:52

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)

Math Is Fun Forum

#1 2012-09-08 14:06:19

Another Triangular Problem

#2 2012-09-08 19:43:40

Re: Another Triangular Problem

#3 2012-09-08 22:38:47

Re: Another Triangular Problem

#4 2012-09-09 01:16:44

Re: Another Triangular Problem

#5 2012-09-09 01:29:50

Re: Another Triangular Problem

#6 2012-09-09 01:34:59

Re: Another Triangular Problem

#7 2012-09-09 01:36:56

Re: Another Triangular Problem

#8 2012-09-09 01:40:16

Re: Another Triangular Problem

#9 2012-09-09 01:54:44

Re: Another Triangular Problem

#10 2012-09-09 03:35:04

Re: Another Triangular Problem

#11 2012-09-09 04:37:18

Re: Another Triangular Problem

#12 2012-09-09 04:55:21

Re: Another Triangular Problem

#13 2012-09-09 06:53:02

Re: Another Triangular Problem

#14 2012-09-09 07:03:19

Re: Another Triangular Problem

#15 2012-09-09 07:15:27

Re: Another Triangular Problem

#16 2012-09-09 07:31:55

Re: Another Triangular Problem

#17 2012-09-10 00:09:22

Re: Another Triangular Problem

#18 2012-09-10 01:35:52

Re: Another Triangular Problem

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