If `r_1 =2 , r_2=3, r_3=6` and r=1 prove that `a=3, b=4, c=5`

r + r_3 + r_1 - r_2 =

In triangleABC , If r_(1), r_(2), r_(3) are exradii opposites to angles A,B and C respectively. Then (1/r_(1) +1/r_(2)) (1/r_(2)+1/r_(3)) (1/r_(3)+1/r_(1)) is equal to

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

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

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

In A B C ,(a b-r_1r_2)/(r_3),w h e r ea ,b ,r_1r_2, r_3, Ra n dr have usual meanings, is equal to (A) R (B) 2R (C) r (D) none of these

If r,r_(1) ,r_(2), r_(3) have their usual meanings , the value of 1/(r_(1))+1/(r_(2))+1/(r_(3)) , is

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]

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

O is the circumcenter of A B Ca n dR_1, R_2, R_3 are respectively, the radii of the circumcircles of the triangle O B C ,O C A and OAB. Prove that a/(R_1)+b/(R_2)+c/(R_3),(a b c)/(R_3)