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

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

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.

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_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 if r_(1) = 36 , r_(2) = 18 and r_(3) = 12 , then the area of the triangle , in square units, is

In a triangle , if r_(1) = 2r_(2) = 3r_(3) , then a/b + b/c + c/a is equal to

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

In Delta ABC , if r_(1) lt r_(2) lt r_(3) , then find the order of lengths of the sides

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 :