(Solved): The circle passing through all three vertices of a triangle is called a circumcircle of the triang ...

The circle passing through all three vertices of a triangle is called a circumcircle of the triangle. The following theorem not only shows that every triangle has a unique circumcircle, but also shows how to construct the circumcircle. Prove that: The three perpendicular bisectors of a triangle are concurrent. Their point of intersection (called the circumcentre) is the centre of a circle (called a circumcircle). Prove this theorem using congruence. In the diagram above, the midpoints of

and

are

and

respectively.