SSC CHSL 2024 PYQ — Question 51

The correct answer is option 3 i.e.  $\sqrt{3}r$.

The center of the circle divides the equilateral triangle into three congruent isosceles triangles.

The angle at the center of the circle for each of these triangles is 360°/3 = 120°

Here, OA = OB = OC = r (Radius)

Let, AB = BC = AC = s

Law of cosines to relate the side length (s) to the radius (r),

s² = r² + r² - 2(r)(r)cos120°

⇒ s² = 2r² - 2r²(-1/2)

⇒ s² = 2r² + r² = 3r²

⇒ s = √(3r²) = √3r

Therefore, the side length of the equilateral triangle is √3r units.