Explanation

From (s−a)+(s−b)+(s−c) = s we get a+b+c = 2s. Expanding the numerator gives (s−a)²+(s−b)²+(s−c)² = 3s²−2s(a+b+c)+(a²+b²+c²) = (a²+b²+c²)−s². As printed, the ratio equals 1 − s²/(a²+b²+c²), which is not constant (it is 1/4 for a = b = c), so the source transcription of the expression appears incomplete. The published official key gives (b) 1, which is retained here. Note: key disputed — verify against the official UPSC key.