Let ABC be a triangle with incenter I and inradius r. Let D, E, and 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 quadrilaterals AFIE, BDIF, and CEID, respectively, Then (r_(1))/(r-r_(1))+(r_(2))/(r-r_(2))+(r_(3))/(r-r_(3))=

Let ABC be a triangle with incenter I and inradius r. Let D, E, and F

1.	Let ABC be a triangle with incenter I and inradius r. Let D, E, and 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 quadrilaterals AFIE, BDIF, and CEID, respectively, Then (r_(1))/(r-r_(1))+(r_(2))/(r-r_(2))+(r_(3))/(r-r_(3))=
Answer» `(r_(1)r_(2)r_(3))/((R-r_(1))(r-r_(2))(r-r_(3)))` `((r-r_(1))(r-r_(2))(r-r_(3)))/(r_(1)r_(2)r_(3))` `((r+r_(1))(r+r_(2))(r+r_(3)))/(r_(1)r_(2)r_(3))` `(r_(1)r_(2)r_(3))/((r+r_(1))(r+r_(2))(r+r_(3)))` ANSWER :A