Expert: Paul Klarreich - 2/13/2011

Question
If a large pipe is placed between a 1 ft. chunck of wood and a 2 ft. chunck of wood that are 6 ft. apart, what is the radius of the pipe?
Thank you so much!

Answer
Questioner:   Carrie
Category:  Advanced Math
Private:  No
 
Subject:  Pre-calculus word problem
Question:  If a large pipe is placed between a 1 ft. chunck of wood and a 2 ft. chunck of wood that are 6 ft. apart, what is the radius of the pipe? Thank you so much!
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      *(-3,2)
      |                                       
      |                                       
      |                                       
      |                                       
      |                                       *(3,1)
      |                                       |
      |                                       |
      |                                       |
      |                                       |
      |                                       |
      |                                       |
-------+-------------------*-------------------+
    (-3,0)               (0,0)                (3,0)




The general equation of a circle is:

x^2 + y^2 + Ax + By + C = 0

Your circle passes through these 3 points:

(-3,2)
(3,1)
(0,0)

1.Substitute each of those points into the circle equation.

2.You will get 3 equations in 3 unknowns - A,B,C.

3.Solve for A,B,C.

4.Use completing the square to reform your equation from the general form (above) to the 'Center-and-Radius' form:

(x - a)^2 + (y - b)^2 = r^2

That should do it.