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Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

 Mar 22, 2024
 #1
avatar+128794 
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ABC  will form a triangle  and the circle is the  circumcumcircle of the triangle

 

radius =   [product of the  sides ] /  [4 area ]

 

semiperimeter  =  [ 8 + 15 + 12 ] / 2=   17.5

 

Area =  sqrt  [ 17.5 ( 9.5) (2.5) (5.5) ] 

 

radius =   [ 8 * 12 * 15 ] / [ 4 sqrt [ 17.5 (9.5)(2.5)(5.5) ] ]  ≈  7.53

 

 

cool cool cool

 

 

 

 

 

 

 

cool cool cool

 Mar 22, 2024

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