+0  
 
-1
95
1
avatar

Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 1$ cm. What is the area of the shaded region?

 

 Mar 19, 2021
 #1
avatar+121003 
+1

Angle  ACB  is a right angle  since its endpoints  lie  on a diameter

 

So

 

AB^2  -  BC^2  =  AC^2

4^2  - 1^2  =  AC^2

16  -  1   =  AC^2

15  = AC^2

sqrt (15)  = AC

 

The   area  of  triangle  ABC   is   AC * BC  /  2 =      sqrt (15)  *  1 /   2     =   sqrt (15)  /  2         (1)

 

Area of circle =  pi  *2^2  =   4 pi     (2)

 

Shaded  area =   (2)  -  (1) =   4pi  - sqrt (15) / 2   ≈    10.63  cm^2

 

 

cool cool cool 

 Mar 19, 2021

5 Online Users

avatar
avatar