The ex-radii `r_(1), r_(2), r_(3)` of a `DeltaABC` are in Hp, show that its sides a,b,c, are in AP.

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

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

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

If r_(2) +r_(3)+ r = r_(1), then show that Delta is right angled.

In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

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)

If a,b,c are in AP and a^(2),b^(2),c^(2) are in HP, then

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then a : b is equal to

In a Delta ABC, show that (a cos A+b cos B+ c cos C)/(a+b+c)= (r )/(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]