If the sides be a,b,c, than find `(r_(1)- r)(r _(2)+r_(3)).`

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))

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

In a triangle ABC, ab and c are the sides of the triangle satisfying the relation r_(1)+r_(2) = r_(3)-r then the perimeter of the triangle

If a,b,c are in AP, then show that r_(1), r_(2), r_(3) are in HP.

If r,r_(1) ,r_(2), r_(3) have their usual meanings , the value of 1/(r_(1))+1/(r_(2))+1/(r_(3)) , is

In any triangle ABC, find the least value of (r_(1) + r_(2) + r_(3))/(r)

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

In triangleABC , If r_(1), r_(2), r_(3) are exradii opposites to angles A,B and C respectively. Then (1/r_(1) +1/r_(2)) (1/r_(2)+1/r_(3)) (1/r_(3)+1/r_(1)) is equal to

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The sides of the triangle are in the ratio

If in a Delta the ex-reddii r_(1) r_(2) r_(3) are in the ratio 1:2:3 then their sides are in the ratio :-