The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. the equation of the circle then changes to (x – 30)2 + (y – 16)2 = (r2)2, and the circle still passes through the origin. what are the values of r1 and r2?

For an equation to pass through the origin, (0,0) must be a solution of the equation. So, for the first one, 



(0, 0) must satisfy the equation and we can solve for the value of r₁ as shown below.






Since the second equation of the circle also passes through the origin, we use the same steps from the first one.





Thus, we have the values for r₁ and r₂ as 20 and 34, respectively.

r₁ = 20 and r₂ = 34

None of the options you showed are it.