GATE 2025 CE (CE1) – Question 9
A circle with center at $(x, y) = (0.5, 0)$ and radius $= 0.5$ intersects with another circle with center at $(x, y) = (1, 1)$ and radius $= 1$ at two points. One of the points of intersection $(x, y)$ is:
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Correct answer: (B) $(0.2, 0.4)$
Explanation
A point must satisfy both $(x - 0.5)^2 + y^2 = 0.25$ and $(x - 1)^2 + (y - 1)^2 = 1$. For $(0.2, 0.4)$ the first gives $0.09 + 0.16 = 0.25$ and the second gives $0.64 + 0.36 = 1$, so it lies on both circles. $(0, 0)$ and $(0.5, 0.5)$ lie on the first circle but give 2 and 0.5 in the second. $(1, 2)$ is not on the first circle.