1. ## radius given a point on circumference

I have a word problem:
A pipe is against a wall. There is a point on the circumference that is both ten inches from the wall and five inches from the ground. Give two possibilities for the radius of the pipe.

I guess that it has something to do with substituting (10,5) in the standard formula for a circle, but that leaves me with three variables.

Any help would be appreciated greatly.

2. Originally Posted by hokusai
I have a word problem:
A pipe is against a wall. There is a point on the circumference that is both ten inches from the wall and five inches from the ground. Give two possibilities for the radius of the pipe.

I guess that it has something to do with substituting (10,5) in the standard formula for a circle, but that leaves me with three variables.

Any help would be appreciated greatly.
Is the pipe running horizontally? ... vertically? ... some other direction???

seems to me the 2" from the ground is not necesssary to solve this unless there is some other info you haven't provided.

3. ## re: skeeter

there is a diagram included, i have attempted to reproduce it:

4. the pipe is tangent to a right angled corner ...

the center of the circle is at the point $\displaystyle (r,r)$

so, the circle's equation is $\displaystyle (x-r)^2 + (y-r)^2 = r^2$

sub in the given values, $\displaystyle x = 10$ and $\displaystyle y = 5$ , and solve for $\displaystyle r$ ... you will get two solutions.

5. wow that seems so much simpler than having the center at say (h,k) and trying to solve (10-h)^2 + (5-k)^2 = r^2
funny how the simplest and most obvious can be so elusive
much thanks