Posted by **Knights** on Friday, March 1, 2013 at 9:14am.

For some positive real number r , the line x+y=r is tangent to the circle x^2+y^2 = r. Find r.

How do we do this? Set equal equations together??

- analytic geometry helps are appreciated -
**drwls**, Friday, March 1, 2013 at 10:23am
r^1/2 is the radius of the circle.

r is the y-intercept of the line

y = r - x.

It is tangent to the circle if

r^2 = 2*(sqrtr)^2

(from Pythagorean rule)

Therefore r^2 = 2r

r = 2

Plot the two functions

y = 2-x and

x^2 + y^2 = 2

You will see that there is tangency at

(sqrt2, sqrt2)

- analytic geometry helps are appreciated -
**Knights**, Friday, March 1, 2013 at 10:38am
thanks a bunch sire

- analytic geometry helps are appreciated -
**Anonymous**, Friday, July 19, 2013 at 6:13pm
Yes set the two equations equal to each other. You then get that r = 2. I'm not going to tell you all of the work because drwls has already answered.

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