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GATE 2025 Chemical Engineering, Q9 · General Aptitude

The correct answer is B, (0.2, 0.4).

Question

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:

  • A. (0, 0)
  • B. (0.2, 0.4)
  • C. (0.5, 0.5)
  • D. (1, 2)

Official answer: (0.2, 0.4)

Why

GATE 2025 official key: (B). Distance from (0.5,0.4)... checking (0.2,0.4): distance to (0.5,0)=0.09+0.16=0.25=0.5(0.5,0)=\sqrt{0.09+0.16}=\sqrt{0.25}=0.5 ✓ (matches radius 0.5); distance to (1,1)=0.64+0.36=1=1(1,1)=\sqrt{0.64+0.36}=\sqrt{1}=1 ✓ (matches radius 1). Both circle equations are satisfied.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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