Question

c. mai wants to construct a regular hexagon inscribed in the circle centered at c. she will follow these instructions. 1. draw the circle centered at d with radius cd. 2. mark the intersection of the circle centered at c, and label that point e. 3. draw the circle centered at e with radius de. 4. mark the intersection of the circle with the circle centered at d, and label that point f. 5. connect abcdef to make a regular hexagon. will these instructions work to finish the hexagon from the construction given? a. yes. b. no.

Explanation:

Step1: Recall hexagon - construction property

A regular hexagon inscribed in a circle can be constructed by using the radius of the circle as the side - length of the hexagon. When we start from a point \(C\) on a circle, draw circles centered at points on the circle with the radius equal to the radius of the original circle, we can find the vertices of the hexagon.

Step2: Analyze the given steps

1. Drawing circles centered at \(D\) with radius \(CD\), at \(C\) with radius \(CD\) etc. and marking the intersection points is a valid way to find the vertices of a regular hexagon inscribed in a circle. Connecting the points \(ABCDEF\) will form a regular hexagon.

Answer:

A. Yes