If I is the incentre and `I _1,I _2,I _3` are the centre of escribed circles of the `triangleABC`. Prove that
`II_1.II_2.II_3 = 16 R^2r`.

If 1 is the incentre and 1_1,1_2,1_3 are the centre of escribed circles of the triangleABC . Prove that II_1,II_2,III_3 = 16 R^2r .

If I_1, I_2, I_3 are the centers of escribed circles of triangle A B C , show that area of triangle I_1I_2I_3=(a b c)/(2r)dot

If I_(1), I_(2), I_(3) are the centers of escribed circles of Delta ABC , show that the area of Delta I_(1) I_(2) I_(3) is (abc)/(2r)

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.

If I is the incenter of A B Ca n dR_1, R_2,a n dR_3 re, respectively, the radii of the circumcircles of the triangles I B C ,I C Aa n dI A B , then prove that R_1R_2R_3=2r R^2dot

If I is the incenter of Delta ABC and R_(1), R_(2), and R_(3) are, respectively, the radii of the circumcircle of the triangle IBC, ICA, and IAB, then prove that R_(1) R_(2) R_(3) = 2r R^(2)

If I_(1) is the centre of the escribed circle touching side BC of !ABC in which angleA=60^(@) , then I_(1) A =

In a Delta ABC , if (II_(1))^(2)+(I_(2)I_(3))^(2)=lambda R^(2) , where I denotes incentre, I_(1),I_(2) and I_(3) denote centres of the circles escribed to the sides BC, CA and AB respectively and R be the radius of the circum circle of DeltaABC . Find lambda .

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_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)))