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,
(9-a)^2+(4-b)^2=r^2(9−a)2+(4−b)2=r2.......(1)(1)
(7-a)^2+(1-b)^2=r^2(7−a)2+(1−b)2=r2..........(2)(2)
(3-a)^2+(6-b)^2=r^2(3−a)2+(6−b)2=r2.........(3)(3)
We have 33 equations with 33 unknowns
From (1)(1) and (2)(2), we get
81-18a+a^2+16-8b+b^2=49-14a+a^2+1-2b+b^281−18a+a2+16−8b+b2=49−14a+a2+1−2b+b2
4a+6b=474a+6b=47
4a+6b=474a+6b=47.............(4)(4)
From (2)(2) and (3)(3), we get
49-14a+a^2+1-2b+b^2=9-6a+a^2+36-12b+b^249−14a+a2+1−2b+b2=9−6a+a2+36−12b+b2
8a-10b=58a−10b=5
8a-10b=58a−10b=5..............(5)(5)
From equations (4)(4) and (5)(5), we get
94-12b=5+10b94−12b=5+10b
22b=8922b=89
b=89/22b=8922
4a=47-6*89/22=47-3*89/11=250/114a=47−6⋅8922=47−3⋅8911=25011, =>⇒, a=250/44=125/22a=25044=12522
The center of the circle is =(125/22,89/22)=(12522,8922)
r^2=(3-125/22)^2+(6-89/22)^2=(59/22)^2+(43/22)^2r2=(3−12522)2+(6−8922)2=(5922)2+(4322)2
=5330/484=5330484
=2665/242=2665242
The area of the circle is
A=pi*r^2=2665/242*pi=34.6A=π⋅r2=2665242⋅π=34.6
