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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: 86,636

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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