Question (Circles)

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2009-02-15 02:03:16 補充：
(a)
First sub y=5-x into C1
(x-3)2 + (5-x)2 = 4
x^2-8x+15=0
x=3 or 5
y=2 or 0
So let A(3,2) B(5,0)
Now C3 with AB as a chord such that the area of the circle is the minimum => AB is the diameter
So centre (4,1) radius^2=8
(x-4)^2+(y-1)^2=8
(b)
The slope of C1C2=1 and the slope of C2C3=1
The slope of AB=-1
So the centres of C1, C2 and C3 are collinear and the line joining them is perpendicular to the chord AB