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 Δ ABC, then ( R + r ) is equal to :

Question

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 Δ ABC, then ( R + r ) is equal to : (A) (9/√2) (B) 7 √2 (C) 2 √2 (D) 3 √2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/cbf6871c489c9be5a97f5cf6cf340025-.png" /> r = OM =(3/√2) sin 30°=(1/2)=( r / R ) ⇒ R =(6/√2) ∴ r + R =(9/√2)

Q. Let the centroid of an equilateral triangle $A BC$ 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 $Δ A BC$ , then $(R + r)$ is equal to :

$\frac{9}{2}$

$72$

$22$

$32$

$r = OM = \frac{3}{2}$
$& sin 3 0^{\circ} = \frac{1}{2} = \frac{r}{R} \Rightarrow R = \frac{6}{2}$
$∴ r + R = \frac{9}{2}$

Q. 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 ΔABC, then (R+r) is equal to :

2​9​

72​

22​

32​