If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord of a circle with centre $(2, 1)$, then the radius of that circle is:
Step-by-Step Solution
Key Concept: The inner circle has centre $(1, 3)$ and radius $2$. Its diameter (length $4$) is a chord of the outer circle with centre $(2, 1)$. Distance from $(2, 1)$ to $(1, 3)$: $\sqrt{5}$. By Pythagoras, outer radius $= \sqrt{2^2 + (\sqrt{5})^2} = 3$.
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Correct Answer: (1)