Question

The vertices A , B , C , D of the triangles are (2 , 1) , (5 , 2) and (3 , 4) respectively . Find the coordinates of the circumcentre and also the radius of the circumcircle

Answer 1

Let P ( x , y ) be the co -ordinates of the centre of the circumcircle
$\therefore P{A}^2=P{B}^{2}andP{B}^2=P{C}^2$
$\therefore 3x+y=12andx+3y=10$
solving these two we get the centre as (13 / 4 , 9 / 5 ) Having found P we can say that
$P{A}^2=r^2=50/16\therefore r=5\sqrt{2}/4$