My question is(r1+r2) (r2+r3) (r1+r3) divided by Rs^2

dear aditi, aruns answer is totally crap and you shall get zero marks for such a solution. he has simply taken a special case of equilateral triangle. but we need to prove for general triangle.

we know the standard formulas:

r1= A/(s – a), r2= A/(s – b), r3= A/(s – c) where A is area of triangle and s is semiperimeter, 2s= a+b+c

R= abc/4A

also, by heron formula

A^2= s(s – a)(s – b)(s – c)

substitute these values and simplify, we get

A^3*abc/R(s(s – a)(s – b)(s – c))^2

= 4A^4/(A^2)^2

= 4A^4/A^4

= 4