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Given an arc with a measure of 60◦ whose endpoints are at (1, 5) and (5, 3), find the area of the circle that contains the arc.

Confusedperson  Nov 4, 2018
 #1
avatar+91213 
+2

Distance between  (1, 5)  and  5, 3)  =

 

sqrt  [  ( 5 - 1)^2 + ( 5 - 3)^2 ]  =

 

sqrt [ 4^2 + 2^2]  =     sqrt [ 20]  

 

And if we connect these two points with a chord as well as drawing two radii to each point from the center of the circle, we will have an equilateral triangle....and since this triangle will have equal sides, the radii will have the same length as the chord

 

So....the area of the circle  =   pi * radius^2    =  pi * ( sqrt(20) ) ^2  =    20 pi units^2   ≈ 62.83 units^2

 

 

 

cool cool cool

CPhill  Nov 4, 2018

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