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:
Options:
(A) (0, 0)
(B) (0.2, 0.4)
(C) (0.5, 0.5)
(D) (1, 2)
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.9)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Number Theory (Divisibility / Remainders)
- Evaluating modular arithmetic congruences for integer problems.
**2. Option Analysis**:
- Option (C) uniquely satisfies the simultaneous modular constraints.
- **Option (C) is CORRECT**.
- **Options (A), (B), and (D) are INCORRECT**: Violate the given remainder conditions.
**3. Final Answer**:
- **Correct Choice**: **C**
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