# area of the shaded area of the circle.

• October 22nd 2010, 10:39 PM
ejaykasai
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.

http://i1209.photobucket.com/albums/.../Photo0267.jpg
• October 22nd 2010, 11:39 PM
CaptainBlack
Quote:

Originally Posted by ejaykasai
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?

Post what you have done.

CB
• October 23rd 2010, 06:31 AM
ejaykasai
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.
• October 23rd 2010, 06:57 AM
HallsofIvy
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.
• October 23rd 2010, 01:37 PM
Soroban

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.