Question

Let ABC be an equilateral triangle with side length a. Let R and r denote the radii of the circumcircle and the incircle of triangle ABC respectively. Then, as a function of a, the ratio R/r

(a) strictly increases

(b) strictly decreases

(c) remains constant

(d) strictly increases for a < 1 and strictly decrease for a > 1

Answer 1

Answer is : (c) remains constant

For an equilateral triangle ABC having side length a. If R and r are radii of the circumcircle and the incircle of triangle ABC respectively, then

which is independent of a and it is constant.