To calculate the area of the circle, we must calculate the radius rr of the circle
Let the center of the circle be O=(a,b)O=(a,b)
Then,
(8-a)^2+(7-b)^2=r^2(8−a)2+(7−b)2=r2.......(1)(1)
(2-a)^2+(1-b)^2=r^2(2−a)2+(1−b)2=r2..........(2)(2)
(5-a)^2+(6-b)^2=r^2(5−a)2+(6−b)2=r2.........(3)(3)
We have 33 equations with 33 unknowns
From (1)(1) and (2)(2), we get
64-16a+a^2+49-14b+b^2=4-4a+a^2+1-2b+b^264−16a+a2+49−14b+b2=4−4a+a2+1−2b+b2
12a+12b=10812a+12b=108
a+b=9a+b=9.............(4)(4)
From (2)(2) and (3)(3), we get
4-4a+a^2+1-2b+b^2=25-10a+a^2+36-12b+b^24−4a+a2+1−2b+b2=25−10a+a2+36−12b+b2
6a+10b=566a+10b=56
3a+5b=283a+5b=28..............(5)(5)
From equations (4)(4) and (5)(5), we get
3(9-b)+5b=283(9−b)+5b=28
27-3b+5b=2827−3b+5b=28
2b=12b=1, =>⇒, b=1/2b=12
a=9-1/2a=9−12, =>⇒, a=17/2a=172
The center of the circle is =(17/2,1/2)=(172,12)
r^2=(2-17/2)^2+(1-1/2)^2=(-13/2)^2+(1/2)^2r2=(2−172)2+(1−12)2=(−132)2+(12)2
=170/4=1704
=85/2=852
The area of the circle is
A=pi*r^2=pi*85/2=133.5A=π⋅r2=π⋅852=133.5
