What is the circumradius of a triangle?

The circumradius of a triangle refers to the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle. This is a fundamental concept in triangle geometry, as it helps to relate various properties of the triangle to its circumcircle.

To visualize this, consider a triangle drawn in a plane. If you draw a circle that perfectly fits around this triangle, touching each vertex exactly once, the radius of that circle is defined as the circumradius.

The circumradius is particularly important in geometric constructions and proofs, such as those involving triangle similarity, trigonometric relationships, and in calculations of the area using the circumradius formula. This makes it a key aspect to understand when studying triangles and their properties.