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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.

 Jun 19, 2024
 #1
avatar+129733 
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The radius will be the circumradius of the triangle ABC

 

semi-perimeter  =  [ 8 + 12 + 15 ] /  2 = 17.5

 

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

 

Radius =   product of the sides  / 4 * area  =  

 

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

 

 

cool cool cool

 Jun 19, 2024

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