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

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

In triangle ABC,(r_(3)+r_(1))sqrt([(rr_(2))/(r_(3)r_(1))])=

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

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_(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)))

(r_2+r_3) sqrt((r r_1)/( r_2r_3)) = a

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

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)