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May 8th, 2012, 07:34 AM  #1 
Member Joined: Apr 2012 Posts: 92 Thanks: 0  Finding area of shaded segment within a circle.
Hello, I have this question to which it's solution I'm not quite sure of. The question is based on a diagram, and I can't really present it but I'll explain it to my very best, thank you very much for trying to understand my bad presentation of the question. The diagram is a circle, with center O and points A and B lying on the circle. Radius is 6cm therefore OA=OB=6cm, such that angle AOB = 79 degrees. Find the area of the shaded segment of the circle contained between the arc AB and the chord [AB]. The solution was a simple sentence, [ (79degrees/360 degrees) x pi x 6^2 ]  [(1/2)(6)(6)sin79] I understand that [(1/2)(6)(6)sin79] was derived from the rule 1/2absinc and we're finding the area of the triangle. Therefore, [ (79degrees/360 degrees) x pi x 6^2 ] must be the area of the sector. However, when I looked up the formula for the area of sector, it's (1/2)(delta)(r)^2, where delta is the angle measured in radians. Primarily, how did [ (79degrees/360 degrees) x pi x 6^2 ] come about then? 
May 8th, 2012, 08:02 AM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,672 Thanks: 741  Re: Finding area of shaded segment within a circle. Quote:
The diagram is a semicircle, with center O and points A and B lying on the semicircle's circumference. Or even this way (since 79 < 90): The diagram is a quartercircle, with center O and points A and B lying on the quartercircle's circumference.  
May 8th, 2012, 08:11 AM  #3 
Member Joined: Apr 2012 Posts: 90 Thanks: 0  Re: Finding area of shaded segment within a circle.
Hahaa yeah thanks! Sorry, I'm not good at phrasing.

May 8th, 2012, 08:14 AM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,672 Thanks: 741  Re: Finding area of shaded segment within a circle. Quote:
 

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area, circle, finding, segment, shaded 
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