Question:
What is the circumference of the regular hexagon?
Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm.
Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
What is the circumference of the regular hexagon?
Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm.
Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
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For a regular hexagon inscribed in a circle, the side length is exactly equal to the radius of the circumcircle.
Updated On: Jun 12, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Even both statements together are not sufficient.
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The Correct Option is A
Solution and Explanation
Concept:
A regular hexagon inscribed in a circle has the special property that each side is equal to the radius of the circumcircle.
Thus,
\[
\text{Side}=R.
\]
Hence perimeter (circumference) of a regular hexagon is
\[
6R.
\]
Step 1: Analyze Statement (I). Given: \[ R=6\text{ cm}. \] Since side length equals radius, \[ s=6\text{ cm}. \] Therefore perimeter is \[ 6s=6\times 6=36\text{ cm}. \] A unique answer is obtained. Statement (I) is sufficient.
Step 2: Analyze Statement (II). Given: Each side subtends \[ 60^\circ \] at the centre. This is true for every regular hexagon and merely confirms the shape. No actual measurement is given. Hence perimeter cannot be determined. Statement (II) is insufficient.
Step 1: Analyze Statement (I). Given: \[ R=6\text{ cm}. \] Since side length equals radius, \[ s=6\text{ cm}. \] Therefore perimeter is \[ 6s=6\times 6=36\text{ cm}. \] A unique answer is obtained. Statement (I) is sufficient.
Step 2: Analyze Statement (II). Given: Each side subtends \[ 60^\circ \] at the centre. This is true for every regular hexagon and merely confirms the shape. No actual measurement is given. Hence perimeter cannot be determined. Statement (II) is insufficient.
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