" 2.Prove that "((1)/(r)-(1)/(r_(1)))((1)/(r)-(1)/(r_(2)))((1)/(r)-(1)/(r_(3)))=(abc)/(Delta^(3))=(4R)/(r^(2)s^(2))

In triangle ABC,((1)/(r)-(1)/(r_(1)))((1)/(r)-(1)/(r_(2)))((1)/(r)-(1)/(r_(3)))=

((1)/(r)+(1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3)))^(2)=(4)/(r)((1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3)))

Prove that (r_(1)(r_(2)+r_(3)))/(sqrt(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)))=a

Prove that r_(1)+r_(2)+r_(3)-r=4R

Prove that r_(1)+r_(2)+r_(3)-r=4R

In a triangle ABC,if (1)/(r_(1)^(2))+(1)/(r_(2)^(2))+(1)/(r_(3)^(2))+(1)/(r^(2))=

Prove that a triangle is right angled if (1-(r_(1))/(r_(2)))(1-(r_(1))/(r_(3))) = 2

In Delta ABC , (1)/(r^(2)) + (1)/( r_1^(2)) +(1)/( r_2^(2)) + (1)/(r_3^(2)) =

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)))