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#1 2013-08-23 15:45:33

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

analystic geometry problems with proofs

1. Let A = (1,2), B = (0,1), and C = (5,0). There exists a point Q and a constant k such that for any point P, PA^2 + PB^2 + PC^2 = 3PQ^2 + k. Find the point Q and the constant k. What is the significance of point Q with respect to triangle ABC?

2. In triangle ABC, AB = AC, D is the midpoint of \overline{BC}, E is the foot of the perpendicular from D to \overline{AC}, and F is the midpoint of \overline{DE}. Prove that \overline{AF} is perpendicular to \overline{BE}.


Genius is one percent inspiration and ninety-nine percent perspiration

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#2 2013-08-23 17:01:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,957

Re: analystic geometry problems with proofs

Hi;

What did you do for the first one?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2015-03-12 13:48:43

SPARKS_CHAN
Member
Registered: 2014-12-05
Posts: 15

Re: analystic geometry problems with proofs

bobbym wrote:

Hi;

What did you do for the first one?

Having trouble with this exact problem. Help?

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#4 2015-03-12 19:58:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,957

Re: analystic geometry problems with proofs


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2015-03-12 20:17:11

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,795

Re: analystic geometry problems with proofs

hi mathstudent2000

Yes, bobbym has correctly recognised these.  thedarktiger posted these last March. Looks like you're getting the same exercises.

You'll find solutions if you do a search on tdt's topics.

Bob


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

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