exradius Sentences

The exradius of a triangle can be calculated using various formulas based on its semiperimeter and area.

In triangle ABC, the exradius opposite to side AB is the radius of the circle tangent to AB and the extensions of AC and BC.

The exradius is an important parameter in the study of triangle geometry and its applications in architecture and design.

When a circle is tangent to one side of a triangle and the extensions of the other two sides, the radius of that circle is the exradius.

The exradius of a triangle is a critical measure used in solving problems related to the external geometry of triangles.

To find the exradius, one can use the formula involving the area of the triangle and its semiperimeter.

The exradius is often used in conjunction with other geometric parameters such as the circumradius and inradius.

In the study of triangle properties, the exradius is a key component in understanding the external angles and their tangential properties.

The exradius can be used to determine the distance from the vertex opposite the side to the point where the excircle touches the side.

When dealing with isosceles triangles, the exradius can be simplified using specific formulas that take into account the symmetric properties of the triangle.

The exradius helps in solving problems related to the tangents drawn from a point to the excircle.

In modular arithmetic, the concept of an exradius can be extended to cyclic polygons, providing a bridge between number theory and geometry.

The exradius plays a crucial role in the construction of triangle centers such as the Gergonne point and the Nagel point.

In the field of computational geometry, the exradius is used in algorithms for approximating the shape of polygons.

The exradius is a fundamental concept in the analysis of polyhedral structures in solid geometry.

When dealing with complex numbers, the exradius can be represented geometrically in the complex plane.

In the context of spherical geometry, the exradius concept can be adapted to measure the radius of the excircle on a sphere.

The exradius is a key measure used in the Voronoi diagram, a partitioning of space into regions based on distance to points in a specific subset of the space.

The exradius is used in the study of geometric inequalities, providing a measure of the balance of the sides of a triangle.