Question

find the coordinates of the circumcentre of a triangle whose virtises are (-3,1) (0,-2) and (1,3)

Answer 1

Circumcentre of a triangle is the point of intersection of all the three perpendicular bisectors of the sides of triangle.  So, the vertices of the triangle lie on the circumference of the circle.  Let the coordinates of the circumcentre of the triangle be (x, y).  (x, y) will the equidistant from the vertices of the triangle.  Using distance formula, , it is obtained:    As (x, y) is equidistant from all the three vertices.  So, D1 = D2 = D3  D1 = D2  Adding equations (1) and (2):  ∴ (3, –3) are the coordinates of the circumcentre of the triangle.