The locus of the midpoint of a chord of the circle $x^2 + y^2 = 4$ which subtends a right angle at the origin is:
Step-by-Step Solution
Key Concept: Let $M = (h, k)$. Since $|OA| = |OB| = 2$ and $\angle AOB = 90^\circ$, triangle $OAB$ is right-isosceles. Then $|OM|^2 = |OA|^2/2 = 2$, so the locus is $x^2 + y^2 = 2$.
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Correct Answer: (3)