Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)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)(r_2-r)(r_3-r)=4R r^2

Prove that : (r_1)/((s-b)(s-c))+(r_2)/((s-c)(s-a))+(r_3)/((s-a)(s-b))=3/r

Let the incircle with center I of A B C touch sides BC, CA and AB at D, E, F, respectively. Let a circle is drawn touching ID, IF and incircle of A B C having radius r_2dot similarly r_1a n dr_3 are defined. Prove that (r_1)/(r-r_1)dot(r_2)/(r-r_2)dot(r_3)/(r-r_3)=(a+b+c)/(8R)

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

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

Prove that r_1+r_2+r_3-r=4R

Prove that r_1+r_2+r_3-r=4R

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))