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## What is the center of an inscribed circle?

The center point of the inscribed circle is called the “incenter.” The incenter will always be inside the triangle.

## Does a polygon inscribed in a circle have to be regular?

Every circle has an inscribed regular polygon of n sides, for any n≥3, and every regular polygon can be inscribed in some circle (called its circumcircle). Not every polygon with more than three sides has an inscribed circle; those polygons that do are called tangential polygons.

## What is an inscribed polygon?

An inscribed polygon might refer to any polygon which is inscribed in a shape, especially: A cyclic polygon, which is inscribed in a circle (the circumscribed circle) A midpoint polygon of another polygon.

If you’re given a convex quadrilateral, a circle can be circumscribed about it if and only the quadrilateral is cyclic. A nice fact about cyclic quadrilaterals is that their opposite angles are supplementary.

## What’s the difference between circumscribed and inscribed?

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 polygons can be circumscribed by a circle?

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

## What are the opposite angles in a cyclic quadrilateral?

The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚.

## Is every parallelogram a cyclic quadrilateral?

Parallelogram: Any parallelogram cannot be cyclic because if any quadrilateral is cyclic, then the sum of the opposite angles must be 180°. But in the case of a parallelogram, the opposite sides are equal, not supplementary. Therefore, it cannot be a cyclic quadrilateral.