ABC is an equilateral triangle and O is its circumcentre. If the side of triangle is 6 cm, then the ∠BOC is:

Correct option is D

Given:

ABC is an equilateral triangle.

O is the circumcenter of triangle ABC.

The side of the triangle is 6 cm.

Solution:

Each interior angle of an equilateral triangle is 60°.

Therefore, ∠BAC = ∠ABC = ∠ACB = 60°.

In this case, arc BC subtends ∠BOC at the center O and ∠BAC at point A on the circumference.

Therefore, ∠BOC = 2 $$\times$$​ ∠BAC.

∠BOC = 2 $$\times$$60° = 120°.

Therefore, ∠BOC is 120°.

Alternate Method:

In an equilateral triangle, the circumcenter coincides with the centroid.

Each of the central angles (like ∠BOC) will be equal. Since there are 360 degrees in a full circle,

each central angle is $$\frac{360°}{3 }$$​= 120°.