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

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

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)

In any Delta ABC, prove that r.r_(1).r_(2).r_(3)=Delta^(2)

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

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

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

" (i) Show that "r+r_(1)+r_(2)-r_(3)=4R cos C

In any A B C , prove that r^2+r1 2+r2 2+r3 2=16 R^2-a^2-b^2-c^2dot

In a triangle ABC, prove that r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2.