Prove that : `(r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)`

Prove that : (r_1-r)/(a) +(r_2-r)/(b) = (c )/(r_3) .

Prove that (r_(1)+r_(2))/(1+cos C)=2R

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

Prove that : (r_1+r_2) tan (C )/(2) = (r_3- r) cot ( C)/(2) = c

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

Prove that r_(1)^(2)+r_(2)^(2) +r_(3)^(3) +r^(2) =16R^(2) -a^(2) -b^(2) -c^(2). where r= in radius, R = circumradius,, r_(1), r_(2), r_(3) are ex-radii.

Prove that (r+r_(1))tan((B-C)/(2))=(r+r_(2))((tan(C-A))/(2))=(r+r_(3))((tan(A-B))/(2))