Equation, Area and Circumference of A circle given equation of the tangent and center

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I don't know how to solve for the Area and Circumference but I know how to solve for the equation but I just wanted to make sure... Any help and explanations would be appreciated :)

Problem: A circle is centered at (2, 1) and tangent to the line x + y=0. Find the general equation of the circle, the area and circumference...

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Let the radius of the circle be r. Then, its equation is $(x – 2)^2 + (y – 1)^2 = r^2$ … (1)

It cuts the line $x + y = 0$ …. (2)

Eliminate y from (1) and (2) to obtain a quadratic equation in x (with the unknown r) … (3)

(2) is tangent to (1) means (3) has only one root. Therefore, solving ⊿ = 0, we get the value of $r^2$.

Then, re-write (1).