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,
(1-a)^2+(5-b)^2=r^2(1−a)2+(5−b)2=r2.......(1)(1)
(7-a)^2+(9-b)^2=r^2(7−a)2+(9−b)2=r2..........(2)(2)
(4-a)^2+(2-b)^2=r^2(4−a)2+(2−b)2=r2.........(3)(3)
We have 33 equations with 33 unknowns
From (1)(1) and (2)(2), we get
1-2a+a^2+25-10b+b^2=49-14a+a^2+81-18b+b^21−2a+a2+25−10b+b2=49−14a+a2+81−18b+b2
12a+8b=130-26=10412a+8b=130−26=104
3a+2b=263a+2b=26.............(4)(4)
From (3)(3) and (2)(2), we get
16-8a+a^2+4-4b+b^2=49-14a+a^2+81-18b+b^216−8a+a2+4−4b+b2=49−14a+a2+81−18b+b2
6a+14b=130-20=1106a+14b=130−20=110
3a+7b=553a+7b=55..............(5)(5)
From equations (4)(4) and (5)(5), we get
26-2b=55-7b26−2b=55−7b, =>⇒, 5b=295b=29, b=29/5b=295
3a=26-2b=26-58/5=72/53a=26−2b=26−585=725, =>⇒, a=24/5a=245
The center of the circle is =(24/5,29/5)=(245,295)
r^2=(1-24/5)^2+(5-29/5)^2=(-19/5)^2+(-4/5)^2r2=(1−245)2+(5−295)2=(−195)2+(−45)2
=361/25+16/25=36125+1625
=377/25=37725
The area of the circle is
A=pi*r^2=pi*377/25=47.38u^2A=π⋅r2=π⋅37725=47.38u2
