Theorem 2

Circumcentre

Definition:

"The point of concurrency of the bisectors of the sides of a triangle is called the circumcentre". It is abbreviated as 'S'.

To determine the circumcentre of a triangle, it is just sufficient to find the point of intersection of any two perpendicular bisectors of the sides of a triangle. The third bisector is bound to pass through it by virtue of the following theorem.

Theorem 2

The perpendicular bisectors of the sides of a triangle pass through the same point.

Note:

In the above theorem, we have proved that OA = OB = OC. That is, if a circle with `O' as centre and radius = OA (or OB or OC) is drawn, this circle will pass through the vertices. A, B, C of the triangle. This circle is called the circumcircle, the centre of circumcircle is called the circumcentre and the radius of circum circle as called the circum radius.