# What is circumscribed and inscribed circles?

What is circumscribed and inscribed circles?

## What is circumscribed and inscribed circles?

A circle is circumscribed about a polygon if the polygon’s vertices are on the circle. For triangles, the center of this circle is the circumcenter. A circle is inscribed a polygon if the sides of the polygon are tangential to the circle.

What is a circumscribed circle in geometry?

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

### How do you solve a circle with a circumscribed triangle?

For a triangle △ABC, let s = 12 (a+b+ c). Then the radius R of its circumscribed circle is R=abc4√s(s−a)(s−b)(s−c).

What does inscribed mean in geometry?

A geometric figure which touches only the sides (or interior) of another figure.

#### How do you draw an inscribed circle?

Construct a perpendicular from the center point to one side of the triangle. Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle!

circumscribed circles. When a circle is placed outside a polygon and each vertex of the polygon lies on the circle, we say that the circle is circumscribed about the polygon. Two examples of circles circumscribed about a triangle and about a square are shown below.

How do you make an inscribed circle in geometry?

This is the so-called inscribed circle. Use one of the points shown above as the midpoint of the circle. This point is called the incenter of the triangle. Use the fact that the inscribed circle must be tangent to the sides of the triangle to construct the circle.

## What is the difference between circumscribed and inscribed shapes?

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. If any vertex fails to touch the circle, then it’s not an inscribed shape.

When a circle is inscribed in a polygon with n sides?

When a circle is inscribed in a polygon with n sides, there will be n points of tangency. When a circle is placed outside a polygon and each vertex of the polygon lies on the circle, we say that the circle is circumscribed about the polygon.