Question 1179502: A circle with a centre of (0,0) is defined by the equation x2 +y2 = 100.
Determine the radius of the circle.
The points A(0, _ ) , B( _ ,0) and C( _ , _ ) are points on the circle. Determine a possible value to fill in each blank for each point. The point C must not contain any zeroes in its coordinates. Provide calculation to show the points lie on the circle.
Use analytic geometry to determine the equations of the perpendicular bisectors of the chords AB and AC.
Show that the point (0,0) is the intersection of the perpendicular bisectors.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Note: The perpendicular bisector of any chord of a circle passes through the center of the circle. So this exercise will show that the two perpendicular bisectors we find intersect at (0,0).
Choose A(0,10), B(10,0), and C(6,8).
Chord AB: slope -1; midpoint (5,5); perpendicular slope 1; equation y=x.
Chord AC: slope -1/3; midpoint (3,9); perpendicular slope 3; equation y=3x.
Point of intersection of AB and AC...
y=x; y=3x --> x=3x --> x=0 --> y=0
The intersection is at (0,0), as we knew it would be.
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