Question 1040661: Find the equation of the circle if a triangle whose sides lie on the lines 3x+4y=8, 3x-4y=32 and x-8=0 inscribed the circle.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Find the intersection points.
From eq. 3,
Substituting into eq. 1,
(8,-4)
Substituting into eq. 2,
(8,-2)
Finally adding eq. 1 and eq. 2,
So,
(20/3,-3)
Now you have three points on the circle, solve for the circle.
Use the general form,
.
.
(8,-4):
4.
.
.
(8,-2):
5.
.
.
(20/3,-3):
6.
Subtracting eq. 5 from eq. 4,
Substituting into eq. 4,
7.
Substituting into eq. 6,
8.
Multiply eq. 7 by -9 and add to eq. 8,
and substituting into eq. 7,
.
.
You can complete the square to get into center-radius form,
Center : ( , )
Radius : 
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.
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