Question

The vertices of a triangle are the points (1, 2), (2, 3), (3, 1). Find the centre and radius of its circumcircle.

Answer 1

Let the coordinates of the triangle be A (1, 2), B (2, 3) and C (3, 1).

If a circle is circumscribing the triangle ABC, then it should pass through the points A, B and C and the centre of this circle, say O should be equidistant from the points A, B and C.

⇒ OA = OB = OC

Let the coordinates of point O be (h, k).

We know that distance between two points is given by:

D =

⇒ OA =

⇒ OB =

⇒ OC =

OA = OB

⇒=

Also, OB = OC

⇒=

Solving (1) and (2), we get:

Thus, the coordinates of the centre of the circumcircle are

Radius of the circle = OA

_{Thus, the radius of the circumcircle is}