# Thread: [SOLVED] Circumference Of A Circle

1. ## [SOLVED] Circumference Of A Circle

A student studying constructions draws a circle of radius x, then places the point of his compass at point A on the circumference of the circle he struck an arc which intersected the side of the circle. He then moved the point of the compass to the intersection point and struck another arc. He repeated this procedure and ended up back at his original point after 6 repetitions

A) Does the final point really coincide with the point where he started (point A)?

B) Why did it take 6 repetitions?

C) Does this mean that the circumference of a circle is equal to 6 times the radius? Justify your reasoning

I said yes for A, and for B I said that the 6 repetitions signified the 6 radians of his circle since the arc length is equal to the radius. But I'm not sure how to answer C

2. Originally Posted by realintegerz
I said yes for A, and for B I said that the 6 repetitions signified the 6 radians of his circle since the arc length is equal to the radius. But I'm not sure how to answer C
C is obviously no. the circumference of a circle is equal to $2\pi r \not = 6r$. But you should justify your answer more than that.

3. Hello, realintegerz!

A student studying constructions draws a circle of radius x,
then places the point of his compass at point A on the circumference of the circle,
he struck an arc which intersected the side of the circle.
He then moved the point of the compass to the intersection point and struck another arc.
He repeated this procedure and ended up back at his original point after 6 repetitions

A) Does the final point really coincide with the point where he started (point A)?

B) Why did it take 6 repetitions?

C) Does this mean that the circumference of a circle is equal to 6 times the radius?]
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The six located points are the vertices of a regular hexagon,
. . which fits perfectly inside the circle.

Six-times-the-radius is the perimeter of that hexagon,
. . not the circumference of the circle.