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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,193

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,193

Re: analystic geometry problems with proofs

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,566

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

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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