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

 Nov 25, 2020
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Note that this means that for any value of r, the two equations must have only one solution. You know that y = r - x, so x^2+(r-x)^2=2r. Expand this, create a quadratic in terms of x, and set the discriminant to be 0. That should give you r.

 Nov 25, 2020

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