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

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

(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))

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

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

show that r_(2)r_(3) +r_(3) r_(1)+ r _(1) r_(2)=s^(2)

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

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