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The line y = 3x - 10 intersects a circle centered at the origin at A and B.  We know the lenght of chord AB is \(18\).  Find the area of the circle.

 Apr 23, 2022
 #1
avatar+122388 
-1

We can find  the distance  from  the origin to the line as

 

l  3(0)  - 1(0) - 10   l  /   sqrt  ( 3^2 + 1^2) =     10 / sqrt 10  =   sqrt 10

 

Half the length of  the  chord  =  9

 

We can form  a right triangle  with legs of sqrt 10   and 9   and hypotenuse,  r

 

The  radius^2 of the circle  is     10 + 81   =  91

 

So....the area =     pi * r^2  =    91 pi   ≈   285.9

 

cool cool cool

 Apr 23, 2022
 #2
avatar+125 
-1

Amaz1ng h0w c0rr3ct y0u @lwa¥§ @®É

 Apr 23, 2022

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