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Find the circumradius of triangle ABC.

 

 Apr 14, 2022
 #1
avatar+55 
-2

we want to find all 3 sides so we can use to circumradius formula, so AD=8 and AC=8√2. Because CDB is a 30 60 90 triangle so CB=16 and finally DB=8√3. We find that AB=8+8√3. The circumradius is \(\boxed{8\sqrt2}\)

 Apr 14, 2022
edited by qjin27  Apr 14, 2022
 #2
avatar+122390 
+1

Just to expand on qjin's  answer

 

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

 

[ ( 8sqrt 2) ( 8 + 8sqrt 3) (16) ]  /   [ 4 * (1/2)(8 +8sqrt 3) * 8 ]  =

 

[      16 * 8sqrt 2   ]  /  [ 16 ]  =

 

8sqrt 2

 

 

cool cool cool

 Apr 14, 2022

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