JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Properties of Triangle

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line

x + y = 3

. If

R

and

r

be the radius of circumcircle and incircle respectively of

△ A B C

, then

(R + r)

is equal to :

Answer: (C)

Solution

In an equilateral triangle the centroid, circumcentre and incentre coincide, so the perpendicular distance from the origin to the side

x + y = 3

is the inradius:

r = \frac{∣0 + 0 - 3∣}{1 ^{2} + 1 ^{2}} = \frac{3}{2}

For an equilateral triangle

R = 2 r

, so

R = \frac{6}{2}

and

R + r = \frac{6}{2} + \frac{3}{2} = \frac{9}{2}

R + r = \frac{9}{2}

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option