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,
#(8-a)^2+(7-b)^2=r^2#.......#(1)#
#(2-a)^2+(1-b)^2=r^2#..........#(2)#
#(5-a)^2+(6-b)^2=r^2#.........#(3)#
We have #3# equations with #3# unknowns
From #(1)# and #(2)#, we get
#64-16a+a^2+49-14b+b^2=4-4a+a^2+1-2b+b^2#
#12a+12b=108#
#a+b=9#.............#(4)#
From #(2)# and #(3)#, we get
#4-4a+a^2+1-2b+b^2=25-10a+a^2+36-12b+b^2#
#6a+10b=56#
#3a+5b=28#..............#(5)#
From equations #(4)# and #(5)#, we get
#3(9-b)+5b=28#
#27-3b+5b=28#
#2b=1#, #=>#, #b=1/2#
#a=9-1/2#, #=>#, #a=17/2#
The center of the circle is #=(17/2,1/2)#
#r^2=(2-17/2)^2+(1-1/2)^2=(-13/2)^2+(1/2)^2#
#=170/4#
#=85/2#
The area of the circle is
#A=pi*r^2=pi*85/2=133.5#