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,
(2-a)^2+(4-b)^2=r^2(2−a)2+(4−b)2=r2.......(1)(1)
(6-a)^2+(5-b)^2=r^2(6−a)2+(5−b)2=r2..........(2)(2)
(4-a)^2+(3-b)^2=r^2(4−a)2+(3−b)2=r2.........(3)(3)
We have 33 equations with 33 unknowns
From (1)(1) and (2)(2), we get
4-4a+a^2+16-8b+b^2=36-12a+a^2+25-10b+b^24−4a+a2+16−8b+b2=36−12a+a2+25−10b+b2
8a+2b=418a+2b=41.............(4)(4)
From (2)(2) and (3)(3), we get
36-12a+a^2+25-10b+b^2=16-8a+a^2+9-6b+b^236−12a+a2+25−10b+b2=16−8a+a2+9−6b+b2
4a+4b=364a+4b=36
a+b=9a+b=9..............(5)(5)
From equations (4)(4) and (5)(5), we get
(41-2b)/8=9-b41−2b8=9−b
41-2b=72-8b41−2b=72−8b
6b=72-416b=72−41, =>⇒, b=31/6b=316
8a=41-2*31/6=41-31/3=92/38a=41−2⋅316=41−313=923, =>⇒, a=23/6a=236
The center of the circle is =(23/6,31/6)=(236,316)
r^2=(2-23/6)^2+(4-31/6)^2=(-11/6)^2+(-7/6)^2r2=(2−236)2+(4−316)2=(−116)2+(−76)2
=170/36=17036
=85/18=8518
The area of the circle is
A=pi*r^2=85/18*pi=14.84A=π⋅r2=8518⋅π=14.84
