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 decreases for a>1​

Answer 1

Given : 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.

To find :  function of a the ratio (R)/(r .     Choose correct option

(A) strictly increases (B) strictly decreases (C) remains constant (D) strictly increases for a<1 and strictly decreases for a>1​

Solution:

Let say a is the length of side of equilateral triangle  

R - radii of the circumcircle  of equilateral triangle  

=> R =  a/√3

r - radii of   the incircle of triangle

r = a/2√3

R/r = (a/√3)/(a/2√3)

=> R/r = 2

R/r = 2 is constant  independent of a

Hence option C is correct  

remains constant

learn More:

prove that if the hypotenuse of a right triangle is h and the radius of ...

https://brainly.in/question/13221257

(iv) A triangle inscribed in a circle and not containing the centre ofthe ...

https://brainly.in/question/15897913