To show that `(1)/(r_(1)^(2))+ (1)/(r_(2)^(2))+ (1)/(r_(3)^(2))+(1)/(r ^(2))=(suma ^(2))/(S^(2))`

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

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

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 r_(1)+r_(2)=c cot ((C)/(2))

In a triangleABC , if 1/r^(2) + 1/r_(1)^(2) + 1/r_(2)^(2) + 1/r_(3)^(2) = (a^(2) + b^(2) + c^(2))/(Delta^(n)) , then n is equal to ………..

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

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

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

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

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)))