Circumcentre of a triangle

To illustrate that perpendicular bisectors of the sides of a triangle concur at a point(called the circumcentre) and it falls inside for an acute-angled triangle, on the hypotenuse of right-angled triangle and outside for an obtuse-angled triangle.

**Circumcentre **of a triangle is the point of intersection of all the three perpendicular bisectors of the sides of a triangle. It is where the "perpendicular bisectors" (lines that are at right angles to the midpoint of each side) meet. The circumcentre of a triangle is equidistant from its vertices and the distance of the circumcentre from each of the three vertices are called circum-radius of the triangle.

- All vertices of triangle are equidistant from circumcentre.
- Circumcentre is also the center of circumcircle.
- For acute angled triangle it lies inside the triangle (see fig(a)).
- For obtuse angled triangle it lies outside the triangle (see fig(c)).
- For right angled triangle it lies at the mid-point of hypotenuse (see fig(b)).

Fig (a) Fig (b)

Fig (c)