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:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2026 Q.10)**
**1. Governing Concept & Domain**:
This question evaluates **Quantitative & Analytical Aptitude** under *General Aptitude* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Quantitative & Analytical Aptitude.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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