Question 88427
The equation of a circle with centre O(0, 0) is x² + y² = 10.  The points C(3, 1) and D(1, -3) are the endpoints of chord CD.  EF right bisects chord CD at G.  Verify that the centre of the circle lies on the right bisector of chord CD
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The coordinates of G are those of the midpoint of CD = [(3+1)/2,(1+-3)/2]=(2,-1)
The slope of CD = (1--3)/(3-1)=2
Therefore the slope of the perpendicular bisector is -1/2
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Find the equation of the line with slope -1/2 thru point (2,-1)
-1=(-1/2)(2)+b
b = 0
EQUATION is y=(-1/2)x
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The center of the circle is given as (0,0)
It is on the line y=(-1/2)x because 0=(-1/2)*0
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Cheers,
Stan H.