In any ` A B C ,` prove that `(r_3+r_1)(r_3+r_2)s in C=2r_3sqrt(r_2r_3+r_3r_1+r_1r_2)`

(r_3+r_1)(r_3+r_2)sinC=2r_3sqrt(r_2r_3+r_3r_1+r_1r_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)(r_2-r)(r_3-r)=4R r^2

In a triangle ABC prove that a(rr_1+r_2r_3)=b(rr_2+r_3r_1)=c(rr_3+r_1r_2)=abc

r + r_3 + r_1 - r_2 =

Prove that : 1/(r_1)+1/(r_2)+1/(r_3)=1/r

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

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

(r_(2)+r_(3))sqrt((r r_(1))/(r_(2)r_(3)))=