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Math Help - Points on Cocentric Circles

  1. #1
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    Points on Cocentric Circles

    There are two concentric circles with center O


    Points on Cocentric Circles-1.jpg
    Known Points A,B,C,O,M, Radius OC=OA=OB=r1 and OC=OA=OB=r2 are also known
    Assumption. M is the mid point of AB and AB , Angle OMB=Angle OMA=90 degree
    To be found Points A, B, C in Cartesian Coordinates
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  2. #2
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    Re: Points on Cocentric Circles

    Hello, tariqchpk!

    There are two concentric circles with center O.

    Click image for larger version. 

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    Given: Points A, B, C, O, M
    . . . . . OC = OA = OB = r,\;OC = OA = OB = R
    . . . . . M is the midpoint of AB and AB.
    . . . . . \angle OMB = \angle OMA = 90^o

    Find points A, B, C in cartesian coordinates.

    Place center O at the origin.

    The larger circle has equation:
    . . x^2 + y^2 \:=\:R^2 \quad\Rightarrow\quad x \:=\:\pm\sqrt{R^2 - y^2}

    Let m = MO.
    The horizontal line has equation:. y = m

    The line and the circle intersect at:
    . . A'\left(\sqrt{R^2-m^2},\:m\right)\,\text{ and }\,B'\left(\text{-}\sqrt{R^2-m^2},\:m\right)

    And we have:. C'(0,\,\text{-}R)

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  3. #3
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    Re: Points on Cocentric Circles

    Dear Soroban

    Thanks for the reply.

    There is a problem in my case i.e. cernter of the circles O is not the origin so what changes be made to accommodate it?
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  4. #4
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    Re: Points on Cocentric Circles

    Quote Originally Posted by tariqchpk View Post
    Dear Soroban

    Thanks for the reply.

    There is a problem in my case i.e. cernter of the circles O is not the origin so what changes be made to accommodate it?
    You are expected to make an effort here. If you understand post #2 you should be able to make the necessary changes yourself.
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