Chapter 10.4, Problem 11WE

a.

To determine

To draw: To sketch the figure of a regular octagon inscribed in a circle.

Explanation of Solution

Given:

A Circle

At first drawing the circle with center $O$ ,

  

Now, drawing a horizontal diameter like this,

  

Now, determining the perpendicular like or the vertical diameter taking halfway grater than the radius and forming the vertical diameter like this,

  

Now drawing the angles with the center and bisecting them like this,

  

Now marking the point and joining them up with line segment.

  

Thus this is the figure of a regular octagon inscribed in a circle.

Conclusion:

Therefore, the figure of a regular octagon inscribed in a circle and the shape is called regular Octagon.

b.

To determine

To find:To determine the figure of an eight pointed star inscribed in a circle.

Explanation of Solution

Given:

A Circle

At first drawing the circle with center $O$ ,

  

Now, drawing a horizontal diameter and vertical diameter with the protector and forming the squarelike this,

  

Now taking the measurement of the radius and putting it on one vertex of square and place a cut outside the circle similarly taking the adjacent vertex placing a cut to intersect both the cut in a single point like this,

  

Now similarly drawing all the intersection point and joining them to the outer part of circle,

  

Now joining all the points,

  

Naming all the sides,

  

Conclusion:

Therefore, the discussed figure above is the figure of an eight pointed star inscribed in a circle.