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.
thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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