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Question 319390: Find the co-ordinate of the center of a circle which passes through the points A(1,2),B(3,-4)& C(5,-6).Also find the radius of the circle.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the perpendicular bisector of a chord of a circle passes through the center
the intersection of two PB's defines the center
the midpoint of chord AB is (2,-1)
___ the slope of AB is -6/2 or -3 , so the slope of the PB is 1/3
___ the equation of the PB (using point-slope) is ___ y + 1 = (1/3)(x - 2)
___ 3y = x - 5
the midpoint of chord BC is (4,-5)
___ the slope of BC is -2/2 or -1 , so the slope of the PB is 1
___ the equation of the PB (using point-slope) is ___ y + 5 = (1)(x - 4)
___ y = x - 9
substituting ___ 3(x - 9) = x - 5 ___ 3x - 27 = x - 5 ___ x = 11
substituting ___ y = (11) - 9 = 2
so the center is (11,2)
looking at point A , the radius is 10
FYI ___ the equation of the circle is ___ (x - 11)^2 + (y - 2)^2 = 100
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