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Find the circumradius of triangle ABC.

 

 Apr 13, 2022
 #1
avatar+124592 
+1

Circumradius =     [product of the sides ] /  [ 4 * area ]

 

Since we have a right triangle the area is easy  =  (1/2)(product of the legs)  =  (1/2)(60)  =  30

Product of the sides  = 5*12*13  =  780

 

Circumradius  =     780  / [ 4 * 30 ]   =  780 / 120  =    6.5

 

This brings up an important point :  In a right triangle the circumradius =  (1/2) ( hypotenuse)

 

So :   (1/2) (13)   = 6.5

 

 

cool cool cool

 Apr 13, 2022
 #3
avatar+578 
+2

you beat me to it CPhill smiley

Vinculum  Apr 13, 2022
 #4
avatar+124592 
+1

Sorry, Viculum  !!!....but, at least our answers agree  !!!!

 

 

cool cool cool

CPhill  Apr 13, 2022
 #2
avatar+578 
+3

(13*5*12)/sqrt((13+5+12)*(5-13+12)*(13-5+12)*(13+5-12)) using circumradius formula:

 

you get 6.5

 Apr 13, 2022

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