# Can a pentagon be inscribed in a circle?

## Can a pentagon be inscribed in a circle?

To inscribe a regular pentagon in a circle, first draw perpendicular radii OA and OB from the center O of a circle. Let C be the midpoint of OB and draw AC. Bisect angle ACO to meet OA at D. Draw a perpendicular DE to OA to the circle.

**What does a polygon inscribed in a circle look like?**

A polygon is inscribed in a circle if all its vertices are points on the circle and all sides are included within the circle. A polygon inscribed within a circle is also referred to as a cyclic polygon. Consider the figure below in which a regular pentagon is inscribed in a circle.

**What is an irregular pentagon shape?**

An irregular pentagon is a shape that has five unequal sides. It is possible to have two or three sides of an irregular pentagon equal in length but not all the sides are equal to each other.

### What is the first step in constructing a regular pentagon inscribed in a circle?

Draw a circle in which to inscribe the pentagon and mark the center point O. Draw a horizontal line through the center of the circle. Mark the left intersection with the circle as point B. Construct a vertical line through the center.

**Can a circle be inscribed or circumscribed about any irregular polygon?**

Most, the vast majority, can neither circumscribe a circle nor be inscribed a circle. b. Some can be inscribed in a circle, but cannot circumscribe a circle.

**Which of the following is an irregular polygon?**

An irregular polygon does not have all its sides equal and not all the angles are equal in measure. Examples of irregular polygons are scalene triangle, right triangle, isosceles triangle, rectangle, parallelogram, irregular pentagon, irregular hexagon, etc.

#### What is a circumcised polygon?

A circle that inscribes a polygon is said to be a incircle into the polygon. The concepts of circumscription and inscription can be extended to three (or more) dimensions.

**How many lines of symmetry does an irregular pentagon have?**

It has four lines of symmetry and four sides. A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides.

**How do you construct a pentagon given the diameter of a circle?**

Constructing a pentagon inscribed in a circle

- Draw a diameter of the circle through the center point and mark its endpoints C and M.
- Construct a perpendicular to CM at the point O.
- Mark the point S where it crosses the circle.
- Find the midpoint L of the segment SO by constructing its perpendicular bisector.