Prove the questions
`a(r r_(1) + r_(2)r_(3)) = b(r r_(2) + r_(3) r_(1)) = c (r r_(3) + r_(1) r_(2))`

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

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Show that (r_(1)+ r _(2))(r _(2)+ r _(3)) (r_(3)+r_(1))=4Rs^(2)

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

In a DeltaABC, r_(1) + r_(2) + r_(3) -r =

Prove that (r_(2) + r_(3))/(1 + cos A) = (r_(3) + r_(1))/(1 + cos B) = (r_(1) + r_(2))/(1+ cos C)

Show that 16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)

If r_(1), r_(2), r_(3) are radii of the escribed circles of a triangle ABC and r it the radius of its incircle, then the root(s) of the equation x^(2)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))x+(r_(1)r_(2)r_(3)-1)=0 is/are :

Prove that 2R cos A = 2R + r - r_(1)

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)))