In a `Delta ABC` if `(R )/(r ) le 2`, then show that the triangle is equilateral.

If in a triangle ABC, cos A +cos B+cos C=3/2 , prove that the triangle is equilateral.

In a triangle ABC sin (A/2) sin (B/2) sin (C/2) = 1/8 prove that the triangle is equilateral

In a triangle ABC , if 2R + r = r_(1) , then

In triangleABC , if R/r le 2 , and a=2, then triangle is equal to (triangle=ar(triangleABC)) .

In a triangle ABC if sinA+sinB+sinC = 3^(3/2)/2 prove that the triangle is equilateral.

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 Delta ABC, 8R^(2) = a^(2) + b^(2) + c^(2) , then the triangle ABC is

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

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

If in a Delta ABC, cosA+ cosB + cosC =3/2. Prove that DeltaABC is an equilateral triangle.