Show that `((1)/(r _(1))+ (1)/(r_(2)))((1)/(r_(2))+(1)/(r _(3)))((1)/(r _(3))+(1)/(r_(1)))=(64 R^(3))/(a ^(2)b^(2) c^(2))`

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

Show that (r_(1)+ r _(2))(r _(2)+ r _(3)) (r_(3)+r_(1))=4Rs^(2)

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

Show that 16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)

Value of 1/(r_(1)^2)'+ 1/(r_(2)^2)+ 1/(r_(3)^2)+ 1/(r_()^2) is :

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

The value of 1/(r_(1)^(2))+1/(r_(2)^(2))+1/(r_(2)^(3))+1/(r^(2)) , is

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

If in a triangle (r)/(r_(1)) = (r_(2))/(r_(3)) , then

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