Math Is Fun Forum

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}.

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Genius is one percent inspiration and ninety-nine percent perspiration

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: analystic geometry problems with proofs

Hi;

What did you do for the first one?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SPARKS_CHAN

Member

Registered: 2014-12-05

Posts: 15

Re: analystic geometry problems with proofs

Hi;

What did you do for the first one?

Having trouble with this exact problem. Help?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: analystic geometry problems with proofs

Hi;

You might try looking here.

http://www.mathisfunforum.com/viewtopic.php?id=20627

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob