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Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 2$ cm. What is the area of the shaded region?

 

 Jun 27, 2018
 #1
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Since the base of triangle  ACB  is a diameter, then  ACB  is a right angle

And we can use the Pythagorean Theorem to find  AC

 

AC =  √[AB^2  - BC^2]  =  √[4^2  - 2^2 ] =  √12  units^2 =  2√3  cm

 

And the area  of triangle ABC  =  1/2 the product of the leg lengths  =

1/2 * AC * BC  =  1/2 (2√3) ( 2)  =   2√3 cm^2   (1) 

 

And the area  of the circle  = pi  * (diameter /2)^2 = pi * (4/2)^2  = pi * 2^2  = 4 pi cm^2  (2)

 

So....the shaded area  =

 

area of the circle - area of triangle ABC  =

 

(2)  - (1)  =

 

[ 4pi - 2√3 ) cm^2   ≈     9.10  cm^2

 

 

cool cool cool

 Jun 27, 2018

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