Prove that `(r+r_1)tan((B-C)/2)+(r+r_2)tan((C-A)/2)+(r+r_3)tan((A-B)/2)=0`

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

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

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

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

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

Prove the questions a(r r_(1) + r_(2)r_(3)) = b(r r_(2) + r_(3) r_(1)) = c (r r_(3) + r_(1) r_(2))

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

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 sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)

Prove that tan^(-1)((x-y)/(1+xy))+tan^(-1)((y-z)/(1+yz))+tan^(-1)((z-x)/(1+zx))=tan^(-1)((x^(r)-y^(r))/(1+x^(r)y^(r)))+tan^(-1)((y^(r)-z^(r))/(1+y^(r)z^(r)))+tan^(-1)((z^(r)-x^(r))/(1+z^(r)x^(r)))