## What is inscribed polygon in math?

An inscribed polygon is a polygon in which all vertices lie on a circle. The polygon is inscribed in the circle and the circle is circumscribed about the polygon. ( It is a polygon in a circle) A circumscribed polygon is a polygon in which each side is a tangent to a circle.

**How do you find the area of an inscribed polygon?**

Use the standard formula: the area of an elementary triangle is half the apothem (a) times the length of a side (s). If the regular polygon has n sides, the apothem and half the side length are a=rcosπn,s=rsinπn.

**What is inscribed regular polygon?**

Inscribed Polygon 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 inscribed circle method?

inscribed circle method is an important method suitable for the circle. with the maximum material condition like an internal bore. The. maximum inscribed circle is determined by three data points. according to the criteria of the maximum inscribed circle.

**What is the inscribed angle formula?**

Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

**What is the arc addition postulate?**

Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

#### How do you inscribe a regular polygon in a circle?

Procedure: Set the compass to the radius of the circle and strike six equidistant arcs about its perimeter. Connect two neighboring intersections to the center of the circle. Bisect the resulting angle. Beginning at the intersection of the bisector and the circle strike six more arcs around the circle.

**What is the difference between inscribed polygon and circumscribed polygon?**

In summary, an inscribed figure is a shape drawn inside another shape. A circumscribed figure is a shape drawn outside another shape. For a polygon to be inscribed inside a circle, all of its corners, also known as vertices, must touch the circle.

**What happens to the inscribed polygon as the number of its sides increases?**

As the number of sides increases, the apothem gets closer and closer to the radius of the circle.

## What happens to the inscribed polygon as the number of its sides increases can we say that a circle is a polygon?

In this question, we know that the polygon is a regular polygon i.e. all sides are equal in length. As the number of sides keeps increasing, the area of the circle enclosed in the regular polygon keeps increasing till the number of sides is infinite (i.e. we get a circle) and it overlaps with the original circle.