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circle question watch

    • Thread Starter

    If given four points on a circle,
    how to find the coordinate of the centre?

    I am assuming that these four points are all on the same circle (?).

    I will give you the basic method:

    join any two points on a circle to form a chord

    find the chord's midpoint

    find the equation of the line going through this midpoint which is perpendicular to the chord

    REPEAT this for two other points on the circle.

    Find the point where these two perpendicular lines intersect and this is the centre of your circle.

    A quick sketch will help you see this.

    (Original post by 0utdoorz)
    If given four points on a circle,
    how to find the coordinate of the centre?
    Choose any three points from the given point.
    Three point always are in a circle.
    Pairs of these point give a chord in the circle.
    The line passing through the midpoint of any chord perpendicularly to the cord is
    passing through the centre of the circle.
    Find the intersection of two line of this type (this will be the centre)
    Calculate the radius of the circle (the distance between the centre and one of the 3 points)
    Write down the equation of the circle.
    Substitute the coordinates of 4th point into the equation.
    If the equation is true then your centre is valid, else the 4 points are not on one circle.
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Updated: September 25, 2011

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