Question

mai wants to construct a regular hexagon inscribed in the circle centered at c. will these instructions finish the hexagon from the construction given? if not, in which step did she first make an error? 1. draw the circle centered at d with radius cd. 2. mark the intersection of the circle with the circle centered at c, and label that point e. 3. draw the circle centered at e with radius eb. 4. mark the intersection of the circle with the circle centered at c, and label that point f. 5. connect abcdef to make a regular hexagon.

Explanation:

Step1: Recall hexagon - circle property

A regular hexagon inscribed in a circle has side - length equal to the radius of the circle.

Step2: Analyze step 1

Drawing a circle centered at D with radius CD is a valid start for constructing a regular hexagon inscribed in a circle centered at C.

Step3: Analyze step 2

Marking the intersection (E) of the two circles is also a valid step.

Step4: Analyze step 3

The error occurs here. When constructing a regular hexagon inscribed in a circle centered at C, all radii used for constructing the points on the circle should be equal to the radius of the original circle centered at C. In step 3, using radius EB is incorrect. It should use the radius of the original circle centered at C.

Step5: Analyze step 4 and 5

Since step 3 is incorrect, steps 4 and 5 will not lead to a correct regular - hexagon construction.

Answer:

She first made an error in step 3.