What is the circumcircle of a triangle?

The circumcircle of a triangle is defined as the circle that passes through all three vertices of the triangle. This definition aligns with the fundamental concept of a circumcircle, which is constructed such that each vertex of the triangle lies precisely on the circumference of the circle. This circle is unique for each triangle and is also known as the circumradius, which can be calculated based on the lengths of the triangle's sides.

In this context, the other options do not correctly describe the circumcircle. The option that refers to a circle that bisects the triangle suggests a division that is not related to circumcircle properties. The inscribed circle, or incircle, specifically pertains to a circle that is contained within the triangle and tangent to its sides, distinguishing it from the circumcircle. Lastly, a circle that connects the midpoints of the sides describes a different geometric construction known as the midsegment circle or the nine-point circle, not the circumcircle. Each of these descriptions highlights aspects of triangles and circles, but only the correct answer accurately defines the circumcircle in relation to a triangle’s vertices.