To determine which image illustrates a circle that is inscribed in a pentagon, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a circle inscribed in a pentagon means the circle will be drawn inside of a pentagon.

The image that illustrates this is as followed.

First understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a rectangle inscribed in a circle means the rectangle will be drawn inside of a circle. 

From here the following image can be constructed.

The diameter of the circle is any and all straight lines that cut the circle in half. Since the rectangle is inscribed in that circle and all corners touch the circle then the diameter of the circle is equivalent to the length of the rectangle's diagonal.

To determine whether this particular statement is true or false, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, for any object to be inscribed in a circle that means all points of that object must also be inside the circle.

Thus the statement, "For an object to be inscribed in a circle only one of its points must lie within the circle." is false.

To determine whether this particular statement is true or false, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, any and all polygons can be inscribed in a circle and circles can be inscribed in all polygons.

Thus, the statement, "Polygons can be both inscribed inside a circle and have circles inscribed inside of them." is true.

To determine which image illustrates a diamond that is inscribed in a circle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a diamond inscribed in a circle means the diamond will be drawn inside of a circle.

The image that illustrates this is as followed.

o determine which image illustrates a circle that is inscribed in a diamond, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a circle inscribed in a diamond means the circle will be drawn inside of a diamond.

The image that illustrates this is as followed.

This is true.  An inscribed figure is one that fits inside another shape; it can touch the sides of the shape it is inside but it cannot cross over these sides.  Below is a circle inscribed in a square.  We could also say that the square is circumscribed about the circle.

The incenter is the intersection of the triangle’s three angle bisectors.  Drawing two of these angle bisectors is sufficient enough to find the incenter.  Below is a figure that illustrates the incenter of a triangle as point A.

Explanation: The steps are shown below along with figures for more explanation

1. Make a point at any point on the circle’s circumference

2. Draw an arc across the circle with a compass that is set to the length of the radius, this will be the next vertex

3. Draw arcs in this fashion until there are six vertices 

4. Label every other vertex so that there are three vertices

5. Connect these three vertices making three equal sides

Explanation: The steps are shown below along with figures for more explanation

1. Given a circle (or draw a circle) draw a line across the diameter

2. Draw a line perpendicular to the diameter that also bisects the diameter

3. Label all points that intersect the circumference of the circle

4. Connect the points on the outer edge of the circle to form the four sides of the square