we know that r= Δ/s,r1=Δ/(s-a),r2=Δ/(s-b),r3=Δ/(s-c)
from above put the value of respective in L.H.S.
then it becomes
=(s-a)/Δ + (s-b)/Δ + (s-c)/Δ
=(s-a)+(s-b)+(s-c)/Δ
= 3s-a-b-c/Δ
=3s-(a+b+c)/Δ
=3s-2s/Δ ( we know that s=a+b+c/2)
= s/Δ
=1/(Δ/s)
= 1/r
= R.H.S proved.
( ashok.khatri.9@facebook.com)