What kind of shape?

Question

To construct this shape, draw a circle. Place the compass on a point on the circle and draw an arc of the same radius as the circle. Now place the compass at the intersection of the arc and the circle and draw an arc. Repeat this process until you have gone around the entire circle. Which of the following shapes is created by connecting all arc and circle intersections with a ruler?

A) Regular pentagon

B) Regular hexagon

C) Regular Octagon

D) Regular Dodecagon

Does anyone else get an octagon?

Answer 1

The answer is $B$, regular hexagon. You'll find six equilateral triangles if you connect all points by lines. Your way to construct the figures gives these equilateral triangles. Do you understand why?

Answer 2

Since the edges of the polygon have the same length as the radius of the circle, the angle subtended by an edge from the center of the circle is one angle of an equilateral triangle; that is, $60^\circ$.

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Since there are $360^\circ$ in a circle, so there are $6$ sides to the polygon.