The correct option is D r=4√63
Given: Length of tangents from A,B,C to the incircle are 4,6,8
We know, length of tangents to incircle are s−a,s−b,s−c which are 4,6,8 respectively.
Hence on adding, we have: 3s−2s=18⇒s=18
∴a=14,b=12 and c=10
Clearly, a,b,c as well as s−a,s−b,s−c are in AP
Hence Δs−a,Δs−b,Δs−c are in HP
i.e r1,r2,r3 are in HP
Now, Δ=√18×4×6×8=24√6
Hence r=Δs=4√63