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Math Help - compass question

  1. #1
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    compass question

    So i have a hw problem that gives a picture of a broken dinner plate with a little bit of a rounded circular edge and then a jagged edge, and I am supposed to find the center of the plate with just a compass and straight edge.
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  2. #2
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    Quote Originally Posted by igottaquestion View Post
    So i have a hw problem that gives a picture of a broken dinner plate with a little bit of a rounded circular edge and then a jagged edge, and I am supposed to find the center of the plate with just a compass and straight edge.
    In an unbroken circle,
    if you joint the centre to any 2 points on the circumference,
    all 3 points then form an isosceles triangle.

    An isosceles triangle is formed of 2 identical back-to-back right-angled triangles, which means that if you bisect the base of an isosceles triangle,
    then join the base midpoint to the 3rd vertex, you will have formed identical right-angled triangles inside the isosceles triangle.

    Going in reverse, if you draw a chord across the round part of the broken plate, then the isosceles triangle base is the line joining the 2 points on the circumference (the chord).
    Hence if you bisect this chord and draw the perpendicular bisector, the circle centre lies on this line.
    Draw a 2nd chord, bisect it, draw a 2nd perpendicular bisector.
    The centre also lies on this line, hence the circle centre is the point of intersection of the perpendicular bisectors of the chords.
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  3. #3
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    Hi igottaquestion,
    here's an illustration.
    Attached Thumbnails Attached Thumbnails compass question-plate-centre.jpg  
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