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Math Help - Finding the diameter of the circle

  1. #1
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    Finding the diameter of the circle

    Write I have been given this problem which I simply cannot do? Any helpers please...

    Here we go:

    A, B and L are points on a circle, centre O
    AB is a chord of the circle
    M is the midpoint of AB
    LOM is the midpoint of AB
    AB = 24cm
    LM = 18cm

    What is the diameter of the circle?
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    LOM is the midpoint of AB
    LOM cannot be the midpoint of AB - the midpoint of a chord should be a point. Maybe you mean that LOM is the mediator (or perpendicular bisector) of AB?
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  3. #3
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    Well spotted sorry I miss wrote it

    A, B and L are points on a circle, centre O
    AB is a chord of the circle
    M is the midpoint of AB
    LOM is a straight line
    AB = 24cm
    LM = 18cm
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  4. #4
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    Quote Originally Posted by Natasha1 View Post
    Well spotted sorry I miss wrote it

    A, B and L are points on a circle, centre O
    AB is a chord of the circle
    M is the midpoint of AB
    LOM is a straight line
    AB = 24cm
    LM = 18cm
    Draw a diagram, place the chord AB, the midpoint M and the centre of the circle O.
    Since LOM is a straight line, LM is perpendicular to AB (being in fact the mediator)

    Look at the triangle AOM (Right angle triangle):

    OA = radius of the circle (R)

    AM=24/2=12 cm

    OM=LM-OL=18-R

    Now apply Pythagoras Theorem in triangle AOM, this will lead you to an equation in R.
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  5. #5
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    Hi natasha,
    LM is the perpendicular bisector of AB
    Let the distance from M to arc AB= x then 12 x12 = 18 x
    Take it from there
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  6. #6
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    This is what I get

    r^2 = (18-r)^2 + 12^2
    r^2 = 324 - 36r - r^2 + 144
    r^2 = 468 -36r

    What next?
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  7. #7
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    Quote Originally Posted by Natasha1 View Post
    This is what I get

    r^2 = (18-r)^2 + 12^2
    r^2 = 324 - 36r - r^2 + 144
    r^2 = 468 -36r

    What next?
    First line is ok, there is a mistake in the second one:

    r^2=324-36r+r^2+144

    324-36r+144=0

    Can you solve it now and find r?
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  8. #8
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    r = 13cm so diameter = 26cm. Where do you get all these braincells from?
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  9. #9
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    Quote Originally Posted by Natasha1 View Post
    r = 13cm so diameter = 26cm. Where do you get all these braincells from?
    Sometimes I wonder myself...lol.
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