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    Zarrin's Avatar
    Zarrin Posts: 9, Reputation: 2
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    #1

    Mar 22, 2007, 06:18 PM
    Find the center of a circle?
    I need to find the center of a circle passing through the points A(-3,1), B(2,4), and C(5,-2). I need to express my answer as an ordered pair.
    My teacher said that you can use the distance formula for each one but that it would take a long time and he said that their was an easier way using chords?

    Thanks for your help!
    asterisk_man's Avatar
    asterisk_man Posts: 476, Reputation: 32
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    #2

    Mar 22, 2007, 06:55 PM
    Look at this image:
    Name: circleCenter.gif Views: 4108 Size: 2.4 KB

    We've got the three points on the circle, a,b,c which define the chords ab and because.
    Find d, the midpoint of ab and e, the midpoint of because.
    Find the line through d and perpendicular to ab, fd
    Find the line through e and perpendicular to because, fe
    Fd and fe will intersect at the circle center, f

    Can you determine your answer from this method?

    I happen to love constructive geometry :)
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