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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- Oct 22nd 2010, 10:39 PMejaykasaiarea 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.

http://i1209.photobucket.com/albums/.../Photo0267.jpg - Oct 22nd 2010, 11:39 PMCaptainBlack
- Oct 23rd 2010, 06:31 AMejaykasai
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.

- Oct 23rd 2010, 06:57 AMHallsofIvy
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.

- Oct 23rd 2010, 01:37 PMSoroban

Since $\displaystyle \angle AOB$ is inscribed in a semicircle: $\displaystyle \angle AOB = 90^o.$

As HallsofIvy pointed out: .$\displaystyle PA = PO = PB = 5$

You can now find the area of sector $\displaystyle AOB$ of the large circle

and the area of right triangle $\displaystyle AOB$,

then determine the area of the unshaded segment.