Understanding Circumscribed Circles | Exploring How Circles Enclose and Touch Shapes

circumscribed

In mathematics, the term “circumscribed” is often used in reference to circles and polygons

In mathematics, the term “circumscribed” is often used in reference to circles and polygons.

When it comes to circles, a circle is said to be circumscribed around a shape if it is drawn in such a way that it encloses and touches all the vertices or points of that shape. In other words, the circle passes through all the corners of the shape and its circumference is tangential to all its sides.

For example, if you have a triangle, you can draw a circle that encompasses the entire triangle, with the triangle’s vertices lying exactly on the circle’s circumference. The circle in this case is said to be “circumscribed” around the triangle.

This concept can also be applied to polygons. A polygon is said to be circumscribed around a circle if all the vertices of the polygon lie on the circle’s circumference. The circle in this case is said to be “circumscribed” around the polygon.

One interesting property of a circle circumscribed around a polygon is that the length of the polygon’s side is equal to the diameter of the circumscribing circle. Additionally, the radius of the circumscribing circle is equal to the perpendicular distance between the circle’s center and any side of the polygon.

Overall, the idea of circumscribed circles is useful in geometry as it helps us understand the relationships between circles and polygons, and it can be used to calculate various geometric properties, such as side lengths and angles.

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