in a triangle abc if r1 is the exradius of

Question

In a triangle ABC, if  r₁ is the exradius of the excircle opposite to A, r₂ is the exradius of the excircle opposite to B and r₃ is the exradius of the excircle opposite to C....

prove that (ar₁+br₂+cr₃)/abc=(1/r)-(1/2R)

where r is the inradius and R is the circum radius.

formulas

r₁=(area of triangle)/(s-a)

r₁=stanA/2