Equilateral triangle inscribed in a circle: An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

Introduction / Context:The circumradius R of an equilateral triangle with side a is given by R = a/√3. This follows from standard geometry or from R = a/(√3) derived via central angles and chord relations.

Given Data / Assumptions:Side a = 6 cm; the triangle is equilateral and inscribed (i.e., the circle is circumcircle).

Concept / Approach:Apply the circumradius formula R = a/√3 directly. Keep the radical form in simplest terms to match options.

Step-by-Step Solution:

Verification / Alternative check:Using R = a/(√3) is equivalent to R = (a√3)/3; substituting a = 6 yields the same 2√3 cm.

Why Other Options Are Wrong:3√2 and 4√3 are too large; √3 is half the correct value.

Common Pitfalls:Confusing inradius r = a√3/6 with circumradius R = a/√3.

Final Answer:2√3 cm