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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.

I drew the diagram and found the centre is (2,3), but how can I work it out mathematically?
2. find the gradients of the lines AB and BC by doing (y2 - y1 / x2 - x1).

then the gradient of the line that bisects that line will be found by changing the sign and putting that value over 1. e.g. if gradient is 3, perpendicular line is -1/3

then find the mid point of each respective line. this is easy, just the mid value of both x and y co-ordinates in each case.

then set up the equation for a straight line for both perpendicular lines: y-y1 = m(x - x1) where y1 and x1 are the values for the midpoints.

You then have two equations and two unknowns (x and y). these solve to (2, 3) as you found out by drawing it.

this point is also the centre of the circle. so you can work out the equation of the circle once you know the distance of this point to one of hte points given.

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