Prove that `(r_1+r_2)/(1+cosC)=2R`

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

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

Prove that r_(1)+r_(2)+r_(3)-r=4R

Prove that r_(1)+r_(2)+r_(3)-r=4R

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

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

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

In any triangle ABC, the value of (r_(1)+r_(2))/(1+cosC) is equal to (where notation have their usual meaning) :

If I is the incenter of Delta ABC and R_(1), R_(2), and R_(3) are, respectively, the radii of the circumcircle of the triangle IBC, ICA, and IAB, then prove that R_(1) R_(2) R_(3) = 2r R^(2)

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