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Thread: Finding the radius of a circle

  1. #1
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    Finding the radius of a circle

    I think I am getting dementia. Anyway:

    Two overlapping circles with radius Ra and Rb with their centers separated by C.

    I know Ra, C and the angle m. Find Rb.

    Finding the radius of a circle-figure-46-maths-forum.jpg
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  2. #2
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    Re: Finding the radius of a circle

    Quote Originally Posted by pastmyprime View Post
    I think I am getting dementia. Anyway: Two overlapping circles with radius Ra and Rb with their centers separated by C. I know Ra, C and the angle m. Find Rb.
    Click image for larger version. 

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    You must know more than that!
    From the drawing it appears as if {R_a} \bot {R_b}. Are we given that?
    If so, how does that help or not?
    Thanks from pastmyprime
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  3. #3
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    Re: Finding the radius of a circle

    let $\theta$ be the top angle of the triangle and $\gamma$ be the angle opposite $R_b$

    using the law of sines

    $\dfrac{R_a}{\sin(m)} = \dfrac{C}{\sin(\theta)}$

    $\sin(\theta) =\dfrac{C \sin(m)}{R_a}$

    $\theta = \arcsin\left(\dfrac{C \sin(m)}{R_a}\right)$

    $\gamma = \pi - m - \theta$

    $\dfrac{R_b}{\sin(\gamma)}=\dfrac{R_a}{\sin(m)}$

    $R_b = \dfrac{R_a \sin(\gamma)}{\sin(m)}$
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  4. #4
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    Re: Finding the radius of a circle

    I am amazed by how generous and helpful people are on this forum.

    The law of sines solved the problem. There are two solutions, but only one is possible in the context (self-winding watches).
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