The correct option is D r1+r2+r3s
We know, r1,r2,r3 are the three exradii respectively.
⇒r1−ra+r2−rb+r3−rc
⇒1a[Δs−a−Δs]+1b[Δs−b−Δs]+1c[Δs−c−Δs]
⇒Δa[s−(s−a)s(s−a)]+Δb[s−(s−b)s(s−b)]+Δc[s−(s−c)s(s−c)]
⇒Δs(s−a)+Δs(s−b)+Δs(s−c)
⇒1s[r1+r2+r3]
Therefore,
⇒r1−ra+r2−rb+r3−rc=r1+r2+r3s