To calculate the area of the circle, we must calculate the radius #r# of the circle
Let the center of the circle be #O=(a,b)#
Then,
#(9-a)^2+(4-b)^2=r^2#.......#(1)#
#(7-a)^2+(1-b)^2=r^2#..........#(2)#
#(3-a)^2+(6-b)^2=r^2#.........#(3)#
We have #3# equations with #3# unknowns
From #(1)# and #(2)#, we get
#81-18a+a^2+16-8b+b^2=49-14a+a^2+1-2b+b^2#
#4a+6b=47#
#4a+6b=47#.............#(4)#
From #(2)# and #(3)#, we get
#49-14a+a^2+1-2b+b^2=9-6a+a^2+36-12b+b^2#
#8a-10b=5#
#8a-10b=5#..............#(5)#
From equations #(4)# and #(5)#, we get
#94-12b=5+10b#
#22b=89#
#b=89/22#
#4a=47-6*89/22=47-3*89/11=250/11#, #=>#, #a=250/44=125/22#
The center of the circle is #=(125/22,89/22)#
#r^2=(3-125/22)^2+(6-89/22)^2=(59/22)^2+(43/22)^2#
#=5330/484#
#=2665/242#
The area of the circle is
#A=pi*r^2=2665/242*pi=34.6#