Question

which equation correctly expresses the relationship between the radius r of a circle and the side - length s of a regular hexagon inscribed in the circle?
a. s = r
b. s = 2r
c. s = r/√2
d. s = r·√3/2

Explanation:

Step1: Analyze inscribed hexagon

A regular hexagon inscribed in a circle can be divided into six equilateral triangles. The radius of the circle is equal to the side - length of these equilateral triangles.

Step2: Determine side - length relationship

Since the side - length \(a\) of the regular hexagon is equal to the side - length of the equilateral triangle, and the radius \(r\) of the circle is also equal to the side - length of the equilateral triangle, we have \(a = r\).

Answer:

A. \(a = r\)