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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: 90,638

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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