What does it mean when a polygon is said to be circumscribed about a circle?

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. For triangles, the center of this circle is the incenter.

When every side of the polygon is tangent to the circle?

When a polygon is inscribed in a circle, it means that each of the vertices of that polygon intersects the circle. When a polygon is circumscribed about a circle, it means that each of the sides of the polygon is tangent to the circle.

What are circumscribed polygons?

In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle). This is a circle that is tangent to each of the polygon’s sides. All triangles are tangential, as are all regular polygons with any number of sides.

How do you tell if a circle can be circumscribed?

Construct the perpendicular bisectors of all four sides of the quadrilateral. If they all cross at the same point, then that point is the circumcenter of the quadrilateral. The radius of the circumcircle is the distance from the circumcenter to any of the four vertices of the quadrilateral.

How do you find the circumscribed circle?

Combining Theorem 3 with Heron’s formula for the area of a triangle, we get: Corollary 3. 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).

How do you circumscribe a circle with any regular polygon?

For Regular Polygons The circumcircle of a regular polygon is the circle that passes through every vertex of the polygon. If the number of sides is 3, then the result is an equilateral triangle and its circumcircle is exactly the same as the one described in Circumcircle of a Triangle.

How do you know if a circle can be circumscribed?

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.

Which figures can be circumscribed by a circle?

The circumscribed circle is the circle drawn outside of any other shapes such as polygon, touching all the vertices of the polygon, and is termed as circumcircle.

How do you tell if a circle can be circumscribed around a quadrilateral?

Which polygons can have circumscribed circles?

All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle’s center is within the polygon.