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Math Help - Calculate perimeter of shaded area

  1. #1
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    Calculate perimeter of shaded area

    Hello guys need some help solving this problem


    MA=MC=4 ; M and O are centers.
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  2. #2
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    Re: Calculate perimeter of shaded area

    There is not enough information to answer the question. If M is the center of the larger figure, then the diagram shows it is not a circle (or else the top of the circle would be at point C instead of a large distance to the left of it). It appears the figure may be an ellipse, but more information would be needed.

    On the other hand, if the diagram is wrong, and the figure centered at M is a circle, then it has a radius of 4. If the figure centered at O is also a circle, you can say it has a radius of $r$. Since the straight line between the centers of two circles that meet in a single point passes through the point of intersection, drawing that line creates a right triangle. The distance from O to B is the radius of the circle, which is $r$, so the distance from A to O is $4-r$. So, you have a triangle with sides of length $4$ and $4-r$ and a hypotenuse of length $4+r$ (the sum of the lengths of the two radii). Solving for $r$, you find $r=1$. Can you figure it out from there?
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  3. #3
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    Re: Calculate perimeter of shaded area

    Yeah the drawing was done wrong(facepalm), anyway I got this


    which is given as the correct answer, Thanks a lot SlipEternal!
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  4. #4
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    Re: Calculate perimeter of shaded area

    That is an approximation, but I am glad it is acceptable. The exact answer is:

    $4 + 3\pi -\arcsin(0.8) - 4\arcsin(0.6)$
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