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

Show that r_(1)+r_(2)=c cot ((C)/(2))

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_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_(2) + r_(3))/(1 + cos A) = (r_(3) + r_(1))/(1 + cos B) = (r_(1) + r_(2))/(1+ cos C)

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

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 (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

In a triangle ABC prove that r_1r_2r_3=r^3 cot^2 (A/2). cot^2 (B/2).cot^2(C/2)