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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,295

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.****No great discovery was ever made without a bold guess. **

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

bobbym wrote:

Hi;

What did you do for the first one?

Having trouble with this exact problem. Help?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,295

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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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