Value of the expression `(b-c)/(r_1)+(c-a)/(r_2)+(a-b)/(r_3)` is equal to 1 (b) 2 (c) 3 (d) 0

The value of (b-c)/(r_(1))+(c-a)/(r_(2))+(a-b)/(r_(3)) is equal to

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

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]

If a,b,c in R^(+), then the minimum value of a(b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2)) is equal to (a)abc (b)2abc (c)3abc (d)6abc

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

If ' O ' is the circum centre of the A B C and R_1,\ R_2,\ R_3 are the radii of the circumcircle of triangle O B C ,\ O C A\ a n d\ O A B respectively then a/(R_1)+b/(R_2)+c/(R_3) has the value equal to (a b c)/(2R^3) (b) (R^3)/(a b c) (c) (4)/(R^2) (d) (a b c)/(R^3)

In any triangle,the minimum value of r_(1)r_(2)r_(3)/r^(3) is equal to 1(b)9(c)27(d) none of these

In a triangle,if r_(1)=2r_(2)=3r_(3), then (a)/(b)+(b)/(c)+(c)/(a) is equal to