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)))`

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_(1) , 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)))

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

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

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

(r_(3)+r_(1))(r_(3)+r_(2))sin C=2r_(3)sqrt(r_(2)r_(3)+r_(3)r_(1)+r_(1)r_(2))

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

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

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

Prove the questions a(r r_(1) + r_(2)r_(3)) = b(r r_(2) + r_(3) r_(1)) = c (r r_(3) + r_(1) r_(2))

r+r_(3)+r_(1)-r_(2)=