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# Cirlces

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1. A circle passes through the points A(-5,4), B(-3,-2), C(1,10).
Find the point of intersection of the perpendicular bisectors of AB and BC.
Find the equation of the circle.

Help on this pls
2. (Original post by Aksa09)
A circle passes through the points A(-5,4), B(-3,-2), C(1,10).
Find the point of intersection of the perpendicular bisectors of AB and BC.
Find the equation of the circle.

Help on this pls
Write equations for the lines AB and BC, then find equations of perpendicular bisectors of these lines then, as the points are in a circle, the perpendicular bisector to a chord on a circle contains the radius (passes through the centre of the circle). So the perpendicular bisector a will intersect at the centre of the circle. Then just use the standard form for the equation of a circle and plug in the centre coordinates and then find radius.
3. (Original post by Ano123)
Write equations for the lines AB and BC, then find equations of perpendicular bisectors of these lines then, as the points are in a circle, the perpendicular bisector to a chord on a circle contains the radius (passes through the centre of the circle). So the perpendicular bisector a will intersect at the centre of the circle. Then just use the standard form for the equation of a circle and plug in the centre coordinates and then find radius.
How do I find equation of the perpendicular bisectors of these lines?
4. (Original post by Aksa09)
How do I find equation of the perpendicular bisectors of these lines?
Well work out the gradient of the lines AB and BC and then do what you normally would to find a line that is perpendicular to another - remember that the perpendicular bisector will go through the midpoints of the lines AB and BC.
5. if two lines are perpendicular the product of their gradients is -1
6. And the bisector means that the perpendicular bisector will go through the midpoint of the line.

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