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)

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 I_(1), I_(2), I_(3) are excentres of the triangle with vertices (0, 0), (5, 12), (16, 12) then the orthocentre of DeltaI_(1)I_(2)I_(3) is

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

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 z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_(1),z_(2),z_(3) are the vertices of an equilational triangle ABC such that |z_(1)-i|=|z_(2)- i| = |z_(3)-i|, then |z_(1)+z_(2)+z_(3)| equals to

Delta I_(1)I_(2)I_(3) is an excentral triangle of an equilateral triangle Delta ABC such that I_(1)I_(2)=4 unit, if DeltaDEF is pedal triangle of DeltaABC , then (Ar(Delta I_(1)I_(2)I_(3)))/(Ar (DeltaDEF))=

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 O be the circumcenter, H be the orthocentre, I be the incenter, and I_1, I_2,I_3 be the excenters of acute-angled A B Cdot Column I Column II Angle subtended by O I at vertex A p. |B-C| Angle subtended by H I at vertex A q. |(B-C)/2| Angle subtended by O H at vertex A r. (B+C)/2 Angle subtended by I_2I_3a tI_1 A q. B/2-C