If in a triangle `r_1=r_2+r_3+r ,` prove that the triangle is right angled.

If r_1=r_2+r_3+r prove that the triangle is right angled .

If r_1=r_2+r_3+r prove that the triangle is right angled .

In a triangle ABC, 8R^2=a^2+b^2+c^2 prove that the triangle is right angled

If in a triangle ABC, r_(1)+r_(2)+r_(3)=9r , then the triangle is necessarily

If in a triangle (1-(r_1)/(r_2))(1-(r_1)/(r_3))=2 then the triangle is right angled (b) isosceles equilateral (d) none of these

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

If in a triangle (r)/(r_(1)) = (r_(2))/(r_(3)) , then

Let ABC be a triangle having O and I as its circumcentre and incentre, respectively. If R and r are the circumradius and the inradius respectively, then prove that (IO) 2 =R 2 −2Rr. Further show that the triangle BIO is right angled triangle if and only if b is the arithmetic mean of a and c.

In A B C , if r\ : r_1: R=2\ : 12\ :5, where all symbols have their usual meaning, then A B C is an acute angled triangle A B C is an obtuse angled triangle A B C is right angled which is not isosceles A B C is isosceles which is not right angled

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