If the sides of a triangle are #a#, #b# and #c#, then the area of the triangle #Delta# is given by the formula
#Delta=sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#
and radius of circumscribed circle is #(abc)/(4Delta)#
Hence let us find the sides of triangle formed by #(9,4)#, #(7,1)# and #(3,9)#. This will be surely distance between pair of points, which is
#a=sqrt((7-9)^2+(1-4)^2)=sqrt(4+9)=sqrt13=3.6056#
#b=sqrt((3-7)^2+(9-1)^2)=sqrt(16+64)=sqrt80=8.9443# and
#c=sqrt((3-9)^2+(9-4)^2)=sqrt(36+25)=sqrt61=7.8102#
Hence #s=1/2(3.6056+8.9443+7.8102)=1/2xx20.3601=10.1801#
and #Delta=sqrt(10.1801xx(10.1801-3.6056)xx(10.1801-8.9443)xx(10.1801-7.8102)#
= #sqrt(10.1801xx6.5745xx1.2358xx2.3699)=sqrt16.01=14.0006#
And radius of circumscribed circle is
#(3.6056xx8.9443xx7.8102)/(4xx14.0006)=4.4976#
And area of circumscribed circle is #3.1416xx(4.4976)^2=63.5496#
