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Math Help - area of the shaded area of the circle.

  1. #1
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    area of the shaded area of the circle.

    The center C of the larger circle lies on another circle whose diameter coincides with the chord AB of the larger circle. Find the area of the shaded region if the length AB measures 10cm.

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  2. #2
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    Quote Originally Posted by ejaykasai View Post
    The center C of the larger circle lies on another circle whose diameter coincides with the chord AB of the larger circle. Find the area of the shaded region if the length AB measures 10cm.

    What have you tried, where are you stuck?

    Post what you have done.

    CB
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  3. #3
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    i got the area of the half circle which is 1/2 pi r^2 but then i don't know how to get the area of the segment to minus it on the half area of the circle.
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  4. #4
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    Since AB, of length 10cm, is a diameter, the radius of the smaller circle is 5 cm. That tells you that the segment from O to P, the center of the smaller circle, is 5 cm. Now, Look at the right triangle formed by OAP. It has legs of 5 and 5 so you can find the length of OA, a radius of the larger circle.
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  5. #5
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    Since \angle AOB is inscribed in a semicircle: \angle AOB = 90^o.

    As HallsofIvy pointed out: . PA = PO = PB = 5

    You can now find the area of sector AOB of the large circle
    and the area of right triangle AOB,
    then determine the area of the unshaded segment.
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