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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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.
http://i1209.photobucket.com/albums/.../Photo0267.jpg
What have you tried, where are you stuck?Quote:
Originally Posted by ejaykasai
Post what you have done.
CB
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.
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.
Sinceis inscribed in a semicircle:
As HallsofIvy pointed out: .
You can now find the area of sectorof the large circle
and the area of right triangle
then determine the area of the unshaded segment.