As shown in the figure, circle C1 with center O1 and radius r1 touches the square
VWXY at points P and Q while circle C2 with center O2 and radius r2 touches the
square VWXY at points R and S. The two circles touch each other at T.
Given r1 = 1 cm and VY̅̅̅̅ = VW̅̅̅̅̅ = 4 cm, r2 = _____ cm.
Options:
(A) 4 - 3√2
(B) 1 + 2√2
(C) 7 - 4√2
(D) 5 + 3√2
Official Answer Key:
MTA
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.10)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Geometry of Circles Inscribed in Squares
- Relationship between radii of touching inscribed circles and square boundary geometry.
**2. Option Analysis**:
- Because ambiguity existed in figure labels or geometric constraints in the printed examination booklet, this question was officially declared **MTA (Marks to All)** by the organizing IIT GATE committee.
- **Official Evaluation**: Full credit awarded to all candidates.
**3. Final Answer**:
- **Official GATE Status**: **MTA (Marks to All)**
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